Mathematics - Areas
Exam Duration: 45 Mins Total Questions : 30
The area bounded by y = \(\frac { sinx }{ x } \)x-axis and the ordinates x=0, x = \(\frac { \pi }{ 4 } \) is
- (a)
= \(\frac { \pi }{ 4 } \)
- (b)
< \(\frac { \pi }{ 4 } \)
- (c)
> \(\frac { \pi }{ 4 } \)
- (d)
\(<\int _{ 0 }^{ \pi /4 }{ \frac { tanx }{ x } dx } \)
If An is the area bounded by y = (1- x2)n and coordinate axes, n\(\in\)N, then
- (a)
An = An-1
- (b)
An < An-1
- (c)
An > An-1
- (d)
An = 2An-1
Area bounded by the curve y = \(\sqrt { (sin[x]+[sinx]) } \) Where [.]denotes the greatest integer function, lines x = 1 and x = \(\frac { \pi }{ 2 } \): and the x-axis is
- (a)
\(\left( \frac { \pi }{ 2 } -1 \right) \) sq unit
- (b)
\(\sqrt { sin1 } \left( \frac { \pi }{ 2 } -1 \right) \) sq unit
- (c)
\(\sqrt { cos1 } \left( \frac { \pi }{ 2 } -1 \right) \) sq unit
- (d)
\(\sqrt { \frac { \pi }{ 2 } } \left( \frac { \pi }{ 2 } -1 \right) \) sq unit
The area between the curve y = 2X4 - X2, the x-axis and the ordinates of two minima of the curve is
- (a)
7/120 sq unit
- (b)
9/120 sq unit
- (c)
11/120 sq unit
- (d)
13/120 sq unit
The area bounded by the x-axis, the curve y = f(x) and the lines x = 1and x = b is equal to \((\sqrt { ({ b }^{ 2 }+1) } -\sqrt { 2 } )\) b>1, then f(x) is
- (a)
\(\sqrt { (x-1) } \)
- (b)
\(\sqrt { (x+1) } \)
- (c)
\(\sqrt { ({ x }^{ 2 }+1) } \)
- (d)
\(\frac { x }{ \sqrt { (1+{ x }^{ 2 }) } } \)
The area bounded by y = x e1xl and lines Iex|= y = 0 is
- (a)
4 sq unit
- (b)
6 sq unit
- (c)
1 sq unit
- (d)
2 sq unit
The area bounded by the curve y = f(x), the x-axis and the ordinates x = 1 and x = b is (b - 1) cos (3b + 4) sq unit. Then f(x) is given by
- (a)
(x - 1) sin (3x + 4)
- (b)
3 (x - 1) sin (3x + 4) + cos (3x + 4)
- (c)
cos (3x + 4) - 3(x - 1) sin (3x + 4)
- (d)
none of the above
polynomial P is positive for x > 0 and the area of the region bounded by P(x), the x-axis and the vertical lines x=0 and x = \(\lambda\) sq unit. en polynomial p(x) is
- (a)
X2 + 2x
- (b)
X2 + 2x + 1
- (c)
X2 + X + 1
- (d)
x3 + 2X2 + 2