JEE Mathematics - Integral Calclus Chapter Sample Question Paper With Answer Key
Exam Duration: 60 Mins Total Questions : 50
The integral \(\int { \frac { { 2 }^{ x+1 }-{ 5 }^{ x-1 } }{ { 10 }^{ x } } } dx\), equals
- (a)
\(-\frac { 2 }{ log5 } ({ 5 }^{ -x })+\frac { 1 }{ 5log2 } ({ 2 }^{ -x })+c\)
- (b)
\(\frac { 2 }{ log5 } ({ 5 }^{ -x })+\frac { 1 }{ 5log2 } ({ 2 }^{ -x })+c\)
- (c)
\(-\frac { 2 }{ log5 } ({ 5 }^{ -x })-\frac { 1 }{ 5log2 } ({ 2 }^{ -x })+c\)
- (d)
NONE OF THESE
\(\int { { (tanx+cotx) }^{ 2 } } dx,\)equals
- (a)
tanx+cotx+c
- (b)
tanx-cotx+c
- (c)
log(tanx+cotx)+c
- (d)
NONE OF THESE
\(\int { \frac { dx }{ \sqrt { x+1 } +\sqrt { x-1 } } } \); equals
- (a)
\(\frac { 1 }{ 3 } [{ (x+1) }^{ 3/2 }+{ (x-1) }^{ 3/2 }]+c\)
- (b)
\(\frac { 1 }{ 3 } [{ (x+1) }^{ 3/2 }-{ (x-1) }^{ 3/2 }]+c\)
- (c)
\(\frac { 2 }{ 3 } [{ (x-1) }^{ 3/2 }+{ (x+1) }^{ 3/2 }]+c\)
- (d)
\(\frac { 1}{ 3 } [{ (x-1) }^{ 3/2 }-{ (x+1) }^{ 3/2 }]\)
The value of the integral \(\int _{ 0 }^{ 100\pi }{ \sqrt { 1+cos\quad 2x\quad dx, } } \) is
- (a)
\(100\sqrt { 2 } \)
- (b)
\(200\sqrt { 2 } \)
- (c)
\(50\sqrt { 2 } \)
- (d)
none of these
The value of the integral
\(\int _{ 0 }^{ 200 }{ (x-[x])dx } \), where [ ] denotes the greastest integer function, is
- (a)
100
- (b)
200
- (c)
50
- (d)
25
The value of integral \(\int _{ 0 }^{ 1/2 }{ \frac { x{ sin }^{ -1 }x }{ \sqrt { 1-{ x }^{ 2 } } } } dx\), is
- (a)
\(\frac { 1 }{ 2 } +\frac { \pi \sqrt { 3 } }{ \sqrt { 2 } } \)
- (b)
\(\frac { 1 }{ 2 } +\frac { \pi }{ 12\sqrt { 3 } } \)
- (c)
\(\frac { 1 }{ 2 } -\frac { \pi \sqrt { 3 } }{ 12 } \)
- (d)
none of these
\(\int { \frac { sinx }{ sin|x-\alpha ) } } dx,\) equals
- (a)
\((x-\alpha )cos\alpha +sin\alpha logsin(x-\alpha )+c\)
- (b)
\((x-\alpha )sin\alpha +sin\alpha logsin|x-\alpha )+c\)
- (c)
\((x-\alpha )sin\alpha +sin\alpha logcos(x-\alpha )+c\)
- (d)
NONE OF THESE
The integral \(\int { \frac { dx }{ x\sqrt { { x }^{ 3 }+1 } } } ,\) equals
- (a)
\(ln\left( \frac { \sqrt { { x }^{ 3 }+1 } +1 }{ \sqrt { { x }^{ 3 }+1 } -1 } \right) \)
- (b)
\(\frac { 2 }{ 3 } ln\left( \frac { \sqrt { { x }^{ 3 }+1 } -1 }{ \sqrt { { x }^{ 3 }+1 } +1 } \right) +c\)
- (c)
\(\frac { 1 }{ 2 } ln\left( \frac { \sqrt { { x }^{ 3 }+1 } -1 }{ \sqrt { { x }^{ 3 }+1 } +1 } \right) +c\)
- (d)
\(\frac { 2 }{ 3 } ln\left( \frac { \sqrt { { x }^{ 3 }+1 }+1 }{ \sqrt { { x }^{ 3 }+1 } -1 } \right) +c\)
The integral \(\int { \frac { dx }{ 9+16{ cos }^{ 2 }x } } ,\) equals
- (a)
\(\frac { 1 }{ 3 } { tan }^{ -1 }\left( \frac { 3tanx }{ 5 } \right) \)
- (b)
\(\frac { 1 }{ 5 } { tan }^{ -1 }\left( \frac { 3tanx }{ 5 } \right) +c\)
- (c)
\( { tan }^{ -1 }\left( \frac { 3tanx }{ 5 } \right) \)
- (d)
\(\frac { 1 }{ 15 } { tan }^{ -1 }\left( \frac { 3tanx }{ 5 } \right) +c\)
\(\int { { tan }^{ 4 }\theta d\theta } ,\) equals
- (a)
\(\frac { { tan }^{ 2 }\theta }{ 3 } +tan\theta +\theta +c\)
- (b)
\(\frac { { tan }^{ 3}\theta }{ 3 } -tan\theta +\theta +c\)
- (c)
\(\frac { { tan }^{ 3}\theta }{ 3 } +cot\theta +\theta +c\)
- (d)
NONE OF THESE
\(\int { \frac { (1+x){ e }^{ x } }{ { cos }^{ 2 }(x{ e }^{ x }) } } dx,\) equals
- (a)
\(tan[(x+1){ e }^{ x }]+c\)
- (b)
\(tan\left( \frac { { e }^{ x } }{ x+1 } \right) +c\)
- (c)
\(tan(x{ e }^{ x })+c\)
- (d)
\(log(x{ e }^{ x })+c\)
\(\int { \frac { (x+1){ (x+logx) }^{ 2 } }{ 2x } } dx,\) equals
- (a)
\(\frac { 1 }{ 6 } { (x+logx) }^{ 3 }+c\)
- (b)
\(\frac { 1 }{ 3 } { (x+logx) }^{ 3 }+c\)
- (c)
\(\frac { 1 }{ 2 } { (x+logx) }^{ 3 }+c\)
- (d)
\(\frac { 1 }{ 8 } { (x+logx) }^{ 3 }+c\)
For any integer n, the integral
\(\int _{ 0 }^{ \pi }{ { e }^{ cos^{ 2 }x }cos^{ 3 }(2n+1)x } \) has the value
- (a)
\(\pi \)
- (b)
1
- (c)
0
- (d)
none of these
If \(y=\sqrt { 5x-6-{ x }^{ 2 } } =1\), then \(\int _{ 2 }^{ 3 }{ y\quad dx } \) equals
- (a)
\(\frac { \pi }{ 4 } \)
- (b)
\(\frac { \pi }{ 2 } \)
- (c)
\( \pi \)
- (d)
none of these
The value of the integral \(\int _{ 0 }^{ \pi /2 }{ sin2xlogtanxdx } \) equals
- (a)
-1
- (b)
0
- (c)
1
- (d)
none of these
The integral \(\int { \frac { sin2x }{ { (a+bcosx) }^{ 2 } } dx } \) equals
- (a)
\(\frac { 1 }{ { b }^{ 2 } } [log(a+bcosx)]+c\)
- (b)
\(-\frac { 1 }{ { b }^{ 2 } } \left[ log(a+bcosx)+\frac { a }{ (a+bcosx) } \right] +c\)
- (c)
\(\frac { 1 }{ { b }^{ 2 } } \left[ log(a+bcosx)-\frac { a }{ (a+bcosx) } \right] +c\)
- (d)
\(-\frac { 2 }{ { b }^{ 2 } } \left[ log(a+bcosx)+\frac { a }{ (a+bcosx) } \right] +c\)
\(\int { \frac { sinx+cosx }{ \sqrt { 1+sin2x } } dx, } \) equals
- (a)
log(sinx+cosx)+c
- (b)
x+c
- (c)
log x+c
- (d)
\(\sqrt { 1+{ sin }^{ 2 }+c } \)
The value of the integral \(\int _{ 0 }^{ \pi /2 }{ \frac { dx }{ 1-2acosx+{ a }^{ 2 } } } a<1\),
- (a)
\(\frac { \pi }{ 2(1-{ a }^{ 2 }) } \)
- (b)
\(\pi (1-{ a }^{ 2 })\)
- (c)
\(\frac { \pi }{ (1-{ a }^{ 2 }) } \)
- (d)
none of these
The value of \(\int _{ 0 }^{ \pi /2 }{ (\sqrt { tanx } } +\sqrt { cotx } )dx\) is
- (a)
\(\frac { \pi }{ 2 } \)
- (b)
\(\pi \sqrt { 2 } \)
- (c)
\(\frac { \pi }{ \sqrt { 2 } } \)
- (d)
none of these
The value of \(\int _{ 0 }^{ 1 }{ { e }^{ { x }^{ 2 } } } dx\) is
- (a)
(0,1)
- (b)
(-1,0)
- (c)
(1,e)
- (d)
none of these
The value of the integral \(\int _{ a }^{ b }{ \frac { |x| }{ x } } dx,a<b\) is
- (a)
a-b
- (b)
a+b
- (c)
b-a
- (d)
\(|b|-|a|\)
If \(F(x)=\int _{ { x }^{ 2 } }^{ { x }^{ 3 } }{ ln(t)dt(x>0) } \) the F'(x) equals,
- (a)
(9x2-4x)ln x
- (b)
(4x+9x2)ln(x)
- (c)
(9x2+4x)ln x
- (d)
none of these
\(\int { \frac { (x-1){ e }^{ x } }{ { (x+1) }^{ 3 } } dx, } \) equals
- (a)
\(\frac { { e }^{ x } }{ (x+1) } +c\)
- (b)
\(\frac { { e }^{ x } }{ { (x+1) }^{ 2 } } +c\)
- (c)
\(\frac { { xe }^{ x } }{ { (x+1) }^{ } } +c\)
- (d)
\(\frac { { x.e }^{ x } }{ { (x+1) }^{ 2 } } +c\)
\(\int { \frac { dx }{ x\sqrt { 1-{ x }^{ 3 } } } } ,\) equals
- (a)
\(\frac { 1 }{ 3 } log\left[ \frac { \sqrt { 1-{ x }^{ 3 } } +1 }{ \sqrt { 1-{ x }^{ 3 } } -1 } \right] +c\)
- (b)
\(\frac { 1 }{ 3 } log\left[ \frac { \sqrt { 1-{ x }^{ 3 } } -1 }{ \sqrt { 1-{ x }^{ 3 } } +1 } \right] +c\)
- (c)
\(\frac { 2 }{ 3 } log\left[ \frac { 1 }{ \sqrt { 1-{ x }^{ 3 } } } \right] +c\)
- (d)
\(\frac { 1 }{ 3 } log\left[ \sqrt { 1-{ x }^{ 3 } } \right] +c\)
f \(\int { \frac { 4{ e }^{ x }+6{ e }^{ -x } }{ 9{ e }^{ x }-4{ e }^{ -x } } } dx=Ax+Blo{ g }_{ e }(9{ e }^{ 2x }-4)+c,\) then values of A,B,C are given by
- (a)
\(A=\frac { -3 }{ 2 } ,B=\frac { 35 }{ 36 } ,C\) is arbitrary constant
- (b)
\(A=\frac { 35}{ 36 } ,B=\frac { -3 }{ 2 } ,C=\frac { 1 }{ 2 } \)
- (c)
\(A=\frac { -35 }{ 36 } ,B=\frac { 3 }{ 2 } ,C=1\)
- (d)
\(A=\frac { 3 }{ 2 } ,B=\frac { 35 }{ 36 } ,C=2 \)
The integral \(\int { \frac { dx }{ { x }^{ 2 }+2xcos\alpha +1 } } ,\) equals
- (a)
\(\frac { 1 }{ cos\alpha } { tan }^{ -1 }\left( \frac { x+sin\alpha }{ cos\alpha } \right) +c\)
- (b)
\(\frac { 1 }{ cos\alpha } { tan }^{ -1 }\left( \frac { x-sin\alpha }{ cos\alpha } \right) +c\)
- (c)
\(\frac { 1 }{ sin\alpha } { tan }^{ -1 }\left( \frac { x-sin\alpha }{ cos\alpha } \right) +c\)
- (d)
\(\frac { 1 }{ sin\alpha } { tan }^{ -1 }\left( \frac { x+sin\alpha }{ cos\alpha } \right) +c\)
\(\int _{ 0 }^{ \pi /2 }{ { sin }^{ 6 }x } { cos }^{ 4 }xdx,\) equals
- (a)
\(\frac { 3\pi }{ 256 } \)
- (b)
\(\frac { \pi }{ 128 } \)
- (c)
\(\frac { \pi }{ 64 } \)
- (d)
none of these
The value of the integral \(\int _{ -1/2 }^{ 1/2 }{ cosxln\left( \frac { 1+x }{ 1-x } \right) } dx\), equals
- (a)
0
- (b)
1
- (c)
\(\frac { 1 }{ 2 } \)
- (d)
\(-\frac { 1 }{ 2 } \)
The integral \(\int _{ 0 }^{ 1 }{ \frac { { tan }^{ -1 }x }{ x } } dx\), equals
- (a)
\(2\int _{ 0 }^{ \pi /2 }{ \frac { t }{ sint } } dt\)
- (b)
\(\int _{ 0 }^{ \pi /2 }{ \frac { t }{ sint } } dt\)
- (c)
\(\frac { 1 }{ 2 } \int _{ 0 }^{ \pi /2 }{ \frac { t }{ sint } } dt\)
- (d)
none of these
\(\int { \frac { x{ ({ tan }^{ -1 }x) }^{ 2 } }{ { (1+{ x }^{ 2) } }^{ 3/2 } } dx, } \) equals
- (a)
\(\frac { [2-{ ({ tan }^{ -1 }x) }^{ 2 }]+2x{ tan }^{ -1 }x+2 }{ \sqrt { 1+{ x }^{ 2 } } } +c\)
- (b)
\(\frac { [2-{ ({ tan }^{ -1 }x) }^{ 2 }]+2x{ tan }^{ -1 }x }{ \sqrt { 1+{ x }^{ } } } +c\)
- (c)
\(\frac { 2-{ ({ tan }^{ -1 }x) }^{ 2 }}{ \sqrt { 1+{ x }^{ 2 } } } \)
- (d)
NONE OF THESE
\(\begin{matrix} lim \\ n\rightarrow \infty \end{matrix}\frac { 1+{ 2 }^{ 4 }+{ 3 }^{ 4 }+...{ n }^{ 4 } }{ { n }^{ 5 } } -\begin{matrix} lim \\ n\rightarrow \infty \end{matrix}\frac { 1+{ 2 }^{ 3 }+{ 3 }^{ 3 }+...{ n }^{ 3 } }{ { n }^{ 5 } } \) equals
- (a)
\(\frac { 1 }{ 30 } \)
- (b)
0
- (c)
\(\frac { 1 }{ 4 } \)
- (d)
\(\frac { 1 }{ 5 } \)
The area of the positive yriangle formed by the positive x-axis and the normal and tangant to the circle x2+y2=4 at \(\left( 1,\sqrt { 3 } \right) \) is
- (a)
\(\sqrt { 3 } \)
- (b)
\(\frac { 1 }{ \sqrt { 3 } } \)
- (c)
\(2\sqrt { 3 } \)
- (d)
none of these
The area of the region bounded by the curves \(y=\sqrt { 5-{ x }^{ 2 } } \) and \(y=|x-1|\), is
- (a)
\(\frac { 1 }{ 2 } +\frac { 5\pi }{ 4 } \)
- (b)
\(\frac { 5\pi }{ 4 } -\frac { 1 }{ 2 } \)
- (c)
\(\frac { 5\pi }{ 4 } \)
- (d)
\(\frac { 1 }{ 2 } \)
The area enclosed with in the curve \(|x|+|y|\)=1 is
- (a)
1
- (b)
1.5
- (c)
2.0
- (d)
none of these
The area bounded by the a-axis part of the curve \(y=\left( 1+\frac { 8 }{ { x }^{ 2 } } \right) \) and the ordinate x=2 and x=4; is divided into the ordinate x=a; then value of a is
- (a)
\(2\sqrt { 2 } \)
- (b)
\(\pm 2\sqrt { 2 } \)
- (c)
\(\pm 2\sqrt { 2 } \)
- (d)
\(\pm 2\)
The integral \(\int { \frac { { x }^{ 3 }+3x+2 }{ { ({ x }^{ 2 }+1) }^{ 2 }(x+1) } dx, } \) equals
- (a)
\(\frac { 3 }{ 2 } { tan }^{ -1 }x+\frac { 1 }{ 4 } log({ x }^{ 2 }+1)-\frac { 1 }{ 2 } log(x+1)+\frac { x }{ 1+{ x }^{ 2 } } +c\)
- (b)
\(\frac { 1 }{ 2 } { tan }^{ -1 }x-\frac { 3 }{ 2 } log({ x }^{ 2 }+1)+\frac { 1 }{ 2 } log(x+1)-\frac { x }{ 1+{ x }^{ 2 } } +c\)
- (c)
\(\frac { 1 }{ 2 } { tan }^{ -1 }x-\frac { 1 }{ 4 } log({ x }^{ 2 }+1)-\frac { 1 }{ 2 } log(x+1)-\frac { x }{ 1+{ x }^{ 2 } } +c\)
- (d)
NONE OF THESE
\(\int { ln(\sqrt { 1-x } +\sqrt { 1+x } ) } dx,\) equals
- (a)
\(xln(\sqrt { 1-x } +\sqrt { 1+x } )-\frac { 1 }{ 2 } x+\frac { 1 }{ 2 } { sin }^{ -1 }x+c\)
- (b)
\(xln(\sqrt { 1-x } +\sqrt { 1+x } )+\frac { 1 }{ 2 } x-\frac { 1 }{ 2 } { sin }^{ -1 }x+c\)
- (c)
\(xln(\sqrt { 1-x } +\sqrt { 1+x } )-\frac { 1 }{ 2 } x-\frac { 1 }{ 2 } { sin }^{ -1 }x+c\)
- (d)
NONE OF THESE
The integral
\(-\int { \frac { { sin }^{ -1 }x-{ cos }^{ -1 }x }{ { sin }^{ -1 }x+{ cos }^{ -1 }x } dx, } \) equals
- (a)
\(\frac { 4 }{ \pi } \left( x{ sin }^{ -1 }-\sqrt { 1-{ x }^{ 2 } } \right) -x+c\)
- (b)
\(\frac { 4 }{ \pi } \left( x{ sin }^{ -1 }+\sqrt { 1-{ x }^{ 2 } } \right) -x+c\)
- (c)
\(x{ sin }^{ -1 }+\sqrt { 1-{ x }^{ 2 } } -x+c\)
- (d)
NONE OF THESE
\(\int { \left( \sqrt { tanx } +\sqrt { cotx } \right) dx, } \) equals
- (a)
\(\sqrt { 2 } { sin }^{ -1 }(sinx+cosx)+c\)
- (b)
\( { sin }^{ -1 }(sinx-cosx)+c\)
- (c)
\(\sqrt { 2 } { sin }^{ -1 }(sinx-cosx)+c\)
- (d)
NONE OF THESE
\(\int { \frac { \sqrt { cos2x } }{ sinx } dx, } \) equals
- (a)
\(\frac { 1 }{ \sqrt { 2 } } log\left( \frac { \sqrt { 2 } +\sqrt { 1-{ tan }^{ 2 }x } }{ \sqrt { 2 } -\sqrt { 1-{ tan }^{ 2 }x } } \right) -\frac { 1 }{ 2 } log\left( \frac { 1+\sqrt { 1-{ tan }^{ 2 }x } }{ 1-\sqrt { 1-{ tan }^{ 2 }x } } \right) +c\)
- (b)
\(\frac { 1 }{ \sqrt { 2 } } log\left( \frac { \sqrt { 2 } +\sqrt { 1-{ tan }^{ 2 }x } }{ \sqrt { 2 } -\sqrt { 1-{ tan }^{ 2 }x } } \right) +\frac { 1 }{ 2 } log\left( \frac { 1+\sqrt { 1-{ tan }^{ 2 }x } }{ 1-\sqrt { 1-{ tan }^{ 2 }x } } \right) +c\)
- (c)
\(\frac { 1 }{ { 2 } } log\left( \frac { \sqrt { 2 } +\sqrt { 1-{ tan }^{ 2 }x } }{ \sqrt { 2 } -\sqrt { 1-{ tan }^{ 2 }x } } \right) +\frac { 1 }{ 2 } log\left( \frac { 1+\sqrt { 1-{ tan }^{ 2 }x } }{ 1-\sqrt { 1-{ tan }^{ 2 }x } } \right) +c\)
- (d)
\(\frac { 1 }{ { 2 } } log\left( \frac { \sqrt { 2 } +\sqrt { 1-{ tan }^{ 2 }x } }{ \sqrt { 2 } -\sqrt { 1-{ tan }^{ 2 }x } } \right) +\frac { 1 }{ 2 } log\left( \frac { 1-\sqrt { 1-{ tan }^{ 2 }x } }{ 1+\sqrt { 1-{ tan }^{ 2 }x } } \right) +c\)
\(\int { \frac { dx }{ (x+2)\sqrt { x+3 } } , } \) equals
- (a)
\(log\left( \frac { \sqrt { x+3 } +1 }{ \sqrt { x-3 } -1 } \right) +c\)
- (b)
\(log\left( \frac { \sqrt { x+3 } -1 }{ \sqrt { x-3 } +1 } \right) +c\)
- (c)
\(\frac { 1 }{ 2 } log\left( \frac { \sqrt { x+3 } -1 }{ \sqrt { x-3 } +1 } \right) +c\)
- (d)
\(\frac { 1 }{ 3 } log\left( \frac { \sqrt { x+3 } -1 }{ \sqrt { x-3 } +1 } \right) +c\)
The integral \(\int { { x }^{ -2/3 }{ (1+{ x }^{ 1/2 }) }^{ -5/3 } } dx,\) equals
- (a)
\(\frac { 3 }{ { (1+{ x }^{ -1/2 }) }^{ 2/3 } } +c\)
- (b)
\(\frac { 1}{ { (1+{ x }^{ -1/2 }) }^{ 2/3 } } +c\)
- (c)
\(\frac { 2 }{ { (1+{ x }^{ -1/2 }) }^{ 2/3 } } +c\)
- (d)
NONE OF THESE
The value of the integral \(\int _{ 0 }^{ \pi }{ \frac { \sqrt { 1+cos\quad 2x } }{ 2 } dx } \), is
- (a)
0
- (b)
-1
- (c)
1
- (d)
2
\(\int _{ 0 }^{ \pi /4 }{ log(1+tan\theta ) } d\theta \), equals
- (a)
\(\frac { \pi }{ 4 } log2\)
- (b)
\(\frac { \pi }{ 8 } log2\)
- (c)
log2
- (d)
\(\frac { \pi }{ 8 } \)
The value of \(\int _{ \pi /2 }^{ 3\pi /2 }{ [2sinx]dx } \), where [ ] represents the greatest integer function, is
- (a)
\(-\pi \)
- (b)
0
- (c)
\(-\frac { \pi }{ 2 } \)
- (d)
\(\frac { \pi }{ 2 } \)
\(\int _{ 0 }^{ 1 }{ |sin2\pi x|dx } \), is equal to
- (a)
0
- (b)
\(-\frac { 1 }{ \pi } \)
- (c)
\(\frac { 1 }{ \pi } \)
- (d)
\(\frac { 2 }{ \pi } \)
The value of the integral \(\int _{ \alpha }^{ \beta }{ \frac { dx }{ (x-\alpha )(\beta -x) } } for\alpha <\beta \), is
- (a)
\(\pi\)
- (b)
\(\frac { \pi }{ 2 } \)
- (c)
\({ sin }^{ -1 }(\alpha /\beta )\)
- (d)
\({ sin }^{ -1 }\left( \frac { \beta }{ 2\alpha } \right) \)
Let f(x) be a function satisfying f'(x)=f(x), with f(0)=1 and g(x) be a function that satisfies f(x)+g(x)=x2
then value of integral ,\(\int { f(x)g(x)dx } \) , is
- (a)
\(e+\frac { { e }^{ 2 } }{ 2 } -\frac { 3 }{ 2 } \)
- (b)
\(e-\frac { { e }^{ 2 } }{ 2 } -\frac { 3 }{ 2 } \)
- (c)
\(e+\frac { { e }^{ 2 } }{ 2 } +\frac { 5 }{ 2 } \)
- (d)
\(e-\frac { { e }^{ 2 } }{ 2 } -\frac { 5 }{ 2 } \)
Let \(f(x)=\int { { e }^{ x }(x-1)(x-2)dx } \). The f decreases in the interval
- (a)
\((-\infty ,-2)\)
- (b)
(-2,1)
- (c)
(1,2)
- (d)
\((2,\infty )\)
Let T>0, be a fixed realnumber.Suppose continuous function, such that for all \(x\in R\) \(f(x+T)=f(x).\)If \(I=\int _{ 0 }^{ T }{ f(x)dx } \) then the value of \(\int _{ 3 }^{ 3+3T }{ f(2x)dx } \)
- (a)
\(\left( \frac { 3 }{ 2 } \right) I\)
- (b)
2I
- (c)
3I
- (d)
6I