∫0π2xsinxdx is equal to : from Mathematics Integrals

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Integrals

Multiple Choice Questions

551.

$\int 13^{x} dx$ is :

$\frac{13^{x}}{\log (13)} + c$
$13^{x + 1} + c$
14x + c
14^{x + 1} + c

552.

$\int_{0}^{\frac{π}{2}} \sin (2 x) \log (\tan (x)) d x$

$π$
$\frac{π}{2}$
1
0

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553.
$\int_{0}^{\frac{π}{2}} xsin (x) dx$ is equal to :

$\frac{π}{4}$

$\frac{π}{2}$

$π$

1

D.

1

$\int_{0}^{\frac{π}{2}} xsin (x) dx = {[- xcos (x)]}_{0}^{\frac{π}{2}} + \int_{0}^{\frac{π}{2}} \cos (x) dx = 0 + {[\sin (x)]}_{0}^{\frac{π}{2}} = 1$

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554.

$\int x^{2} {(ax + b)}^{- 2} dx$ is equal to :

$\frac{2}{a^{2}} (x - \frac{b}{a} \log (ax + b))$ + c
$\frac{2}{a^{2}} (x - \frac{b}{a} \log (ax + b)) - \frac{x^{2}}{a (ax + b)}$
$\frac{2}{a^{2}} (x + \frac{b}{a} \log (ax + b)) - \frac{x^{2}}{a (ax + b)} + c$
$\frac{2}{a^{2}} (x + \frac{b}{a} \log (ax + b)) - \frac{x^{2}}{a (ax + b)} + c$

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555.

If f(t) is an odd function, then $\int_{0}^{x} f (t) dt$ is :

an odd function
an even function
neither even nor odd
0

556.

$\int e^{- \log (x)} dx$ is equal to :

e^{- log(x)} + C
- xe^{- log(x)} + C
e^log(x) + C
$\log |x| + C$

557.

$\int \frac{a^{\frac{x}{2}}}{\sqrt{a^{- x} - a^{x}}} dx$ is equal to :

$\frac{1}{\log (a)} \sin^{- 1} (a^{x}) + c$
$\frac{1}{\log (a)} \tan^{- 1} (a^{x}) + c$
$2 \sqrt{a^{- x} - a^{x}} + c$
$\log (a^{x} - 1) + c$

558.

If g(x) = $\frac{f (x) - f (- x)}{2}$ defined over [- 3, 3], and f(x) = 2x² - 4x + 1, then $\int_{- 3}^{3} g (x) dx$ is equal to :

0
4
- 4
8

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559.

$\int \frac{\sin (x)}{\sin (x - a)} dx$ is equal to :

$xcos (a) - \sin (a) \log (\sin (x - a)) + c$
$xsin (a) + c$
$xsin (a) + \sin (a) \log (\sin (x - a)) + c$
$xcos (a) + \sin (a) \log (\sin (x - a)) + c$

560.

$\int \frac{f' (x)}{f (x) \log [f (x)]} dx$ is equal to :

$\frac{f (x)}{\log (f (x))}$
f(x) . log(f(x)) + c
$\log [\log (f (x))] + c$
$\frac{1}{\log [\log (f (x))]}$ + c

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