### Mathematics - Define Integrals and Its Application

#### Question - 1

$\int^2_0\ e^2\ dx$ is equal to

• A $e^2-1$
• B $e^4-1$
• C $e^3-e^2$
• D $e-1$

#### Question - 2

$\int^{\pi/2}{tan^2\ x\over 1+tan^2\ x}dx$ is equal to

• A $\infty$
• B 0
• C $\pi\over4$
• D $\pi\over2$

#### Question - 3

$\int^{\pi\over 4}_0{sin^2x.cos^2\ x\over (sin^3x+cos^3\ x)^2}dx$ is equal to

• A $1\over 6$
• B $1\over 12$
• C $1\over 4$
• D $1\over 24$

#### Question - 4

$\int^{\pi\over 2}_0{sin^nx\over sin^nx+cos^nx}dx$ is equal to

• A $\pi\over 4$
• B $\pi\over 2$
• C $\pi\over 3$
• D $\pi\over 6$

#### Question - 5

The value of integral $\int^{2\pi}_0e^x\ sin({{\pi\over 4}+{\pi\over 2}})dx$ is

• A ${\sqrt2\over 5}(e^{2\pi+1})$
• B ${-\sqrt2\over 5}(e^{2\pi+1})$
• C ${-\sqrt2\over 5}(e^{2\pi-1})$
• D ${\sqrt2\over 5}(e^{2\pi-1})$

#### Question - 6

$\int^3_2\ {2x^5+x^4-2x^3+2x^2+1\over (x^2+1)(x^4-1)}dx$ is equal to

• A ${1\over 2}({log6+{1\over5}})$
• B ${1\over 2}({log6-{1\over5}})$
• C $-{1\over 2}({log6+{1\over5}})$
• D ${1\over 3}({log6-{1\over5}})$

#### Question - 7

Find the value of $\int^3_1|(x-1)(x-2)(x-3)|dx.$

• A $1\over 3$
• B $1\over 2$
• C $9\over 4$
• D $9\over 5$

#### Question - 8

Find the value of $\int^{/pi}_0\ {sin2kr\over sin\ x}dx$, where $k\in I.$

• A $\pi\over2$
• B $\pi$
• C $3\pi\over2$
• D 0

#### Question - 9

$\int^{\pi/4}_0\ {sin\ x+cos\ x\over 9+16\ sin2x }dx$ is equal to

• A $in\ 3\over 20$
• B $In\ 3\over 40$
• C $In\ 3\over 60$
• D $In\ 3\over 100$

#### Question - 10

$\int^{\pi}_0{x\ tan\ x\over sec\ x + tan\ x}dx$ is equal to

• A ${\pi\over 2}(\pi-2)$
• B ${\pi}(\pi-2)$
• C ${\pi\over 4}(\pi-2)$
• D ${\pi\over 4}(\pi+2)$