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Integrals

Multiple Choice Questions

What is $\int e^{xln (a)} dx = ?$

$\frac{a^{x}}{\ln (a)} + c$
$\frac{e^{x}}{\ln (a)} + c$
$\frac{e^{x}}{\ln (ae)} + c$
$\frac{{ae}^{x}}{\ln (a)} + c$

$\int_{0}^{\frac{π}{2}} |\sin (x) - \cos (x)| d x = ?$

0
$2 (\sqrt{2} - 1)$
$2 \sqrt{2}$
$2 (\sqrt{2} + 1)$

3.
$\int_{0}^{\frac{π}{2}} e^{\sin (x)} \cos (x) d x = ?$

e + 1

e - 1

e + 2

e

e - 1

$\int_{0}^{\frac{π}{2}} e^{\sin (x)} \cos (x) d x Let, \sin (x) = t \cos (x) dx = dt if x = 0, t = \sin (0) = 0 if x = \frac{π}{2}, t = \sin (\frac{π}{2}) = 1 ∴ \int_{0}^{1} e^{t} d t = {[e^{t}]}_{0}^{1} = e^{1} - e^{0} = e - 1$

$What is \int \ln (x^{2}) dx = ?$

$2 xln (x) - 2 x + c$
$\frac{2}{x} + c$
$2 xln (x) + c$
$\frac{2 \ln (x)}{x} - 2 x + c$

$What is \int_{0}^{π} e^{x} \sin (x) d x = ?$

$\frac{e^{π} + 1}{2}$
$\frac{e^{π} - 1}{2}$
$e^{π} + 1$
$\frac{e^{π} + 1}{4}$

$What is \int_{1}^{e} xln (x) d x = ?$

$\frac{e + 1}{4}$
$\frac{e^{2} + 1}{2}$
$\frac{e - 1}{2}$
$\frac{e^{2} - 1}{4}$

$What is \int_{0}^{\sqrt{2}} [x^{2}] d x equal to (where [.] is the greatest integer function) ?$

$\sqrt{2} - 1$
$1 - \sqrt{2}$
$2 (\sqrt{2} - 1)$
$\sqrt{3} - 1$

$What is \int \frac{dx}{2^{x} - 1} = ?$

$\ln (2^{x} - 1) + c$
$\frac{\ln (1 - 2^{- x})}{\ln (2)} + c$
$\frac{\ln (2^{x} - 1)}{2 \ln (2)} + c$
$\frac{\ln (1 + 2^{- x})}{\ln (2)} + c$

$What is the value of \int_{\frac{- π}{4}}^{\frac{π}{4}} (\sin (x) - \tan (x)) d x ?$

$- \frac{1}{\sqrt{2}} + \ln (\frac{1}{\sqrt{2}})$
$\frac{1}{\sqrt{2}}$
0
$\sqrt{2}$

10.

$If \int_{a}^{b} x^{3} d x = 0 and \int_{a}^{b} x^{3} d x = \frac{2}{3}, then what are the values of a and b respectivley ?$

- 1, 1
1, 1
0, 0
2, - 2

Previous Year Papers

Test Series

Test Yourself

Multiple Choice Questions

3. ∫0π2esinxcosxdx = ? e + 1 e - 1 e + 2 e

3.
$\int_{0}^{\frac{π}{2}} e^{\sin (x)} \cos (x) d x = ?$

e + 1

e - 1

e + 2

e