MCQs of સંકલન | GUJCET MCQ

સંકલન MCQs

MCQs of સંકલન

Showing 101 to 110 out of 440 Questions

101.

\int 5^{5^{x}} 5^{x} d x

= _____ + c

(a)	${(\log_{e} 5)}^{2} 5^{5^{x}}$
(b)	$5^{5^{x}} (\log_{e} 5)$
(c)	$5^{5^{x}}$
(d)	$\frac{5^{5^{x}}}{{(\log_{e} 5)}^{2}}$

102.

\int \frac{x^{3}}{x^{8} + 1} d x

= _____ + c

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

103.

\int \frac{(\sin x)^{\frac{5}{2}}}{(\cos x)^{\frac{9}{2}}} d x

= _____ + c

(a)	$- \frac{2}{5} (\tan x)^{\frac{5}{2}}$
(b)	$\frac{2}{5} (\tan x)^{\frac{5}{2}}$
(c)	$\frac{2}{7} (\tan x)^{\frac{7}{2}}$
(d)	$- \frac{2}{7} (\tan x)^{\frac{7}{2}}$

104.

\int x^{n x} (1 + \log x) d x

= _____ + c, (n ≠ 0)

(a)	$\frac{x^{(x - 1) x}}{n - 1}$
(b)	$\frac{x^{(n - 1) x}}{n - 1}$
(c)	$\frac{x^{n x}}{n}$
(d)	આપેલ પૈકી એક પણ નહી.

105.

\int \frac{d x}{(2 x - 7) \sqrt{x^{2} - 7 x + 12}}

= _____ + c, 2x > 7

(a)	2sec^-1 (2x-7)
(b)	sec^-1 (2x-7)
(c)	$\frac{1}{2}$ sec^-1 (2x-7)
(d)	આપેલ ઉકેલમાંથી એક પણ નહી.

106.

\int \frac{3 \tan \frac{x}{3} - \tan^{3} \frac{x}{3}}{1 - 3 \tan^{2} \frac{x}{3}} d x

= _____

(a)	$- \log \|\sec x\| + c$
(b)	$- \log \|\cos x\| + c$
(c)	$\sec^{2} x + c$
(d)	$\log \|\tan x\| + c$

107.

\int \frac{1}{x^{2} (x^{4} + 1)^{\frac{3}{4}}} d x

= _____ + c

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

108.

\int \frac{\sin^{8} x - \cos^{8} x}{1 - 2 \sin^{2} x \cos^{2} x} d x

= _____ + c

(a)	-sinx cosx
(b)	sinx cosx
(c)	sin2x
(d)	cos2x

109.

\int \frac{\sin^{2} x}{\cos^{6} x} d x

= _____ + c

(a)	$\frac{1}{3} \tan^{3} x + \frac{1}{5} \tan^{5} x$
(b)	$\frac{1}{3} \cot^{3} x + \frac{1}{5} \cot^{5} x$
(c)	$\frac{1}{3} \sin^{3} x + \frac{1}{3} \cos^{7} x$
(d)	આપેલ પૈકી એક પણ નહી.

110.

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

= _____ + c

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

Showing 101 to 110 out of 440 Questions