MCQs of Integrals

Showing 131 to 140 out of 403 Questions

131.

\int \frac{1}{e^{x} + 1} d x

= _____

132.

\int \frac{x^{3} + 4 x - 3}{x^{2} + 4} d x A x^{2} + B \tan^{- 1} \frac{x}{2} + c

then A+B = _____ where A,B

\in

133.

\int \frac{d x}{(2 x + 3) \sqrt{x^{2} + 3 x + 2}}

= _____ + c where $x > - \frac{3}{2}$

(a) $4 s e c^{- 1} (2 x + 3)$

(b) $2 s e c^{- 1} (2 x + 3)$

(c) $\frac{1}{2} s e c^{- 1} (2 x + 3)$

(d) $s e c^{- 1} (2 x + 3)$

134.

\int \frac{\sin x - x \cos x}{x^{2} + x \sin x} d x

= _____ + c

(a) $\log |\frac{x + \sin x}{x}|$

(b) $\log |\frac{x}{x + \sin x}|$

(c) $\log |x^{2} + x \sin x|$

(d) $\log |x + x \sin x|$

135.

\int \frac{\sin x + \cos x}{\sin (x - a)}

dx = _____ + c

(a)	(sin a + cos a) x+ (cos a - sin a) log \| sin (x -a)\|
(b)	(sin a + cos a) log \|sin (x -a)\|+ (cos a - sin a) x
(c)	(sin a - cos a) log \|sin (x -a)\|+ (cos a + sin a) x
(d)	(sin a - cos a) log \|sin (x -a)\|+ (cos a - sin a) x

136.

\int_{0}^{π} e^{s i n^{2} x} . c o s^{3} (2 n + 1) x . d x

= _____ (Where n is some integer)

137.

\int_{- 1}^{1} x |x| d x

= _____

138.

The value of

\int_{- 2}^{2} (a x^{3} + b x + c) d x

depends on _____

139.

\int_{0}^{\frac{π}{4}} \tan^{2} x d x =

_____

140.

\int_{\frac{π}{6}}^{\frac{π}{3}} \frac{d x}{\sin 2 x} =

_____

Showing 131 to 140 out of 403 Questions