MCQs of સંકલન | GUJCET MCQ

સંકલન MCQs

MCQs of સંકલન

Showing 151 to 160 out of 428 Questions

151.

\int \frac{dx}{e^{x} - e^{- x}}

=_____+c

(a)	$\frac{1}{2} \log \|\frac{e^{x} - 1}{e^{x} + 1}\|$
(b)	$\tan^{- 1} (e^{x})$
(c)	$\frac{1}{2} \log \|\frac{e^{x} + 1}{e^{x} - 1}\|$
(d)	$\tan^{- 1} (e^{2 x})$

152.

\int \frac{x^{2} dx}{(x + x \log x)^{3}}

= _____ + c

(a)	$3 \log \|x + x \log x\|$
(b)	$- \frac{\log x}{2 (1 + \log x)^{2}}$
(c)	$- \frac{1}{2 (1 + \log x)^{2}}$
(d)	$\frac{3 (1 + \log x)}{x^{3}}$

153.

\int \frac{dx}{3 \cos 2 x + 5}

=_____c

(a)	$\frac{1}{4} \tan^{- 1} (\frac{1}{2} \tan x)$
(b)	$\frac{1}{2} \tan^{- 1} (\frac{1}{2} \tan x)$
(c)	$\frac{1}{2} \tan^{- 1} (\frac{1}{4} \tan x)$
(d)	$\frac{1}{4} \tan^{- 1} (\frac{1}{4} \tan x)$

154.

\int \frac{\tan x}{16 + 25 \tan^{2} x}

dx = _____ c

(a)	$\frac{4}{5} \tan^{- 1} (\frac{5 \tan x}{4})$
(b)	$\frac{1}{20} \tan^{- 1} (\frac{5 \tan x}{4})$
(c)	$\frac{1}{18} \log (4 + 9 \tan^{2} x)$
(d)	$\frac{1}{18} \log \|(16 \cos^{2} x + 25 \sin^{2} x)\|$

155.

જો

\int \frac{\sin^{4} x}{\cos^{2} x} d x = p x + q \sin 2 x + r \tan x + c,

તો

_____

(a)	$p = - \frac{3}{2}, q = \frac{1}{4}, r = 1$
(b)	$p = \frac{1}{4}, q = - \frac{3}{2}, r = 1$
(c)	$p = - 3, q = \frac{1}{2}, r = 1$
(d)	$p = \frac{3}{2}, q = - \frac{1}{4}, r = 1$

156.

\int \frac{dx}{(16 - x^{2})^{\frac{3}{2}}}

=_____+c

(a)	$\frac{x}{4 \sqrt{16 - x^{2}}}$
(b)	$\frac{x}{16 \sqrt{16 + x^{2}}}$
(c)	$\frac{x}{16 \sqrt{16 - x^{2}}}$
(d)	$\frac{x}{(16 - x^{2})^{\frac{3}{2}}}$

157.

\int \frac{x^{2} + 1}{x^{4} - 6 x^{2} + 1} d x =_____+ c

(a)	$x \tan^{- 1} (\frac{x^{2} - 1}{2 x})$
(b)	$\frac{1}{4} \log \|\frac{x^{2} - 2 x - 1}{x^{2} + 2 x - 1}\|$
(c)	$\tan^{- 1} (\frac{x^{2} - 1}{2 x})$
(d)	$\frac{1}{4} \log \|\frac{x^{2} + 2 x - 1}{x^{2} - 2 x - 1}\|$

158.

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

(a)	$\log (1 + e^{x}) + c$
(b)	$\log (\frac{e^{x} + 1}{e^{x}}) + c$
(c)	$\log (\frac{e^{x}}{e^{x} + 1}) + c$
(d)	$\log (1 - e^{- x}) + c$

159.

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

તો

A + B =_____

જ્યાં

A, B \in R .

(a)	2
(b)	-1
(c)	$- \frac{1}{2}$
(d)	$\frac{1}{2}$

160.

\int \frac{\sin 2 x}{p \cos^{2} x + q \sin^{2} x} d x =_____+ c

(a)	$\frac{1}{p^{2} + q^{2}} \log \|p \cos^{2} x + q \sin^{2} x\|$
(b)	$(q - p) \log \|p \cos^{2} x + q \sin^{2} x\|$
(c)	$\frac{1}{p - q} \log \|p \cos^{2} x + q \sin^{2} x\|$
(d)	$\frac{q}{p} \log \|p \sin 2 x + q \cos 2 x\|$

Showing 151 to 160 out of 428 Questions