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Integrals

Multiple Choice Questions

531.

$\int \frac{1}{\sin (x) \cos (x)} dx$ is equal to

$\log |\tan (x)| + C$
$\log |\sin (2 x)| + C$
$\log |\sec (x)| + C$
$\log |\cos (x)| + C$

532.

$\int \frac{2 x + \sin (2 x)}{1 + \cos (2 x)} dx$ is equal to

$x + \log (\tan (x)) + C$
$xlog |\tan (x)| + C$
$xtan (x) + C$
$x + \tan (x) + C$

533.

$\int \frac{1}{8 \sin^{2} (x) + 1} dx$ is equal to

$\sin^{- 1} (\tan (x)) + C$
$\frac{1}{3} \sin^{- 1} (\tan (x)) + C$
$\frac{1}{3} \tan^{- 1} (3 \tan (x)) + C$
$\tan^{- 1} (3 \tan (x)) + C$

534.

$\int_{0}^{\frac{π}{2}} \log (\frac{\cos (x)}{\sin (x)}) dx$ is equal to

$\frac{π}{2}$
$\frac{π}{4}$
$π$
0

535.

The value of $\int_{- 1}^{2} 4 x^{2} |x| d x$ is equal to

536.
The value of $\int_{2}^{4} (x - 2) (x - 3) (x - 4) dx$ is equal to

$\frac{1}{2}$

2

3

0

$Let I = \int_{2}^{4} (x - 2) (x - 3) (x - 4) dx = \int_{2}^{4} (x - 3) (x^{2} - 6 x + 8) dx = \int_{2}^{4} (x - 3) ({(x - 3)}^{2} - 1) dx = \int_{2}^{4} ({(x - 3)}^{3} - (x - 3)) dx = {[\frac{{(x - 3)}^{4}}{4} - \frac{{(x - 3)}^{2}}{2}]}_{2}^{4} = 0$