MCQs of Integrals | GUJCET MCQ

Integrals MCQs

MCQs of Integrals

Showing 91 to 100 out of 421 Questions

91.

Integration of even function is _____ function

(a)	odd.
(b)	even.
(c)	increasing
(d)	none of these.

92.

\int \frac{1 + \cos x}{\cos x (1 - \cos x)} d x =_____+ c

(a)	$\log \|s e c x + \tan x\| - 2 \tan \frac{x}{2}$
(b)	$\log \|s e c x + \tan x\| - 2 c o t \frac{x}{2}$
(c)	$\log \|s e c x + \tan x\| + 2 \tan \frac{x}{2}$
(d)	$\log \|s e c x + \tan x\| + 2 c o t \frac{x}{2}$

93.

\int \frac{\sqrt[3]{t a n x}}{s i n x c o s x} d x =_____+ c

(a)	$\frac{\sqrt[3]{t a n x}}{3}$
(b)	$\frac{\sqrt[3]{c o t x}}{3}$
(c)	$3 \sqrt[3]{c o t x}$
(d)	$3 \sqrt[3]{\tan x}$

94.

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

(a)	$\frac{1}{2 \sqrt{2}} \log \|\tan (\frac{π}{8} + x)\|$
(b)	$- \frac{1}{2 \sqrt{2}} \log \|\tan (\frac{π}{8} - x)\|$
(c)	$\frac{1}{2 \sqrt{2}} \log \|\tan (\frac{3 π}{8} + x)\|$
(d)	$- \frac{1}{2 \sqrt{2}} \log \|\tan (\frac{3 π}{8} - x)\|$

95.

\int \frac{d x}{{(1 - \sin x)}^{\frac{1}{2}}} =_____+ c

(a)	$\sqrt{2} \log \|\tan (\frac{π}{8} - \frac{x}{4})\|$
(b)	$- \sqrt{2} \log \|\tan (\frac{π}{8} - \frac{x}{4})\|$
(c)	$\sqrt{2} \log \|\tan (\frac{3 π}{8} - \frac{x}{4})\|$
(d)	$- \sqrt{2} \log \|\tan (\frac{3 π}{8} - \frac{x}{4})\|$

96.

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

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

97.

\int \frac{e^{x}}{e^{2 x} - 4 e^{x} + 7} d x =_____+ c

(a)	$\frac{1}{\sqrt{3}} s e c^{- 1} (\frac{e^{x} - 2}{\sqrt{3}})$
(b)	$\tan^{- 1} (e^{x} - 2)$
(c)	$\frac{1}{2 \sqrt{3}} \tan^{- 1} (\frac{e^{x} - 2}{\sqrt{3}})$
(d)	$\frac{1}{\sqrt{3}} \tan^{- 1} (\frac{e^{x} - 2}{\sqrt{3}})$

98.

\int x^{4 x} (1 + \log x) d x =_____+ c

(a)	$\frac{x^{5 x}}{5}$
(b)	$\frac{x^{4 x}}{4}$
(c)	$x^{4 x}$
(d)	$x^{5 x}$

99.

\int \frac{f' (x)}{\sqrt{f (x)}} d x

= _____ +

c; f (x) \neq 0

(a)	$\frac{1}{2} \sqrt{f (x)}$
(b)	$2 \sqrt{f (x)}$
(c)	$\frac{1}{2} f (x)$
(d)	$2 f (x)$

100.

\int f (x) d x =_____+ c; f (x) = |\begin{matrix} 2007 & 2008 \\ 2007 x & 2008 x \end{matrix}|

(a)	$x$
(b)	$\frac{x^{2}}{2}$
(c)	constant
(d)	does not exist

Showing 91 to 100 out of 421 Questions