MCQs of સંકલન | GUJCET MCQ

સંકલન MCQs

MCQs of સંકલન

Showing 171 to 180 out of 440 Questions

171.

જો

\int \frac{1 + \cos 4 x}{c o t x - \tan x} d x = A \cos 4 x + B,

તો A અને Bના મુલ્યો _____

(a)	$A = \frac{1}{8}, B \in R$
(b)	$A = - \frac{1}{8}, B \in R$
(c)	$A = \frac{1}{4}, B \in R$
(d)	આ પૈકી એક પણ નહિ

172.

જો

\int \frac{d x}{x + x^{5}} = f (x) + c,

તો

\int \frac{x^{4}}{x + x^{5}} d x =_____

(a)	$\log_{e} x - f (x) + c$
(b)	$f (x) + \log_{e} x + c$
(c)	$f (x) - \log_{e} x + c$
(d)	આ પૈકી એક પણ નહિ

173.

\int \frac{d x}{{\{{(x - 1)}^{3} {(x + 2)}^{5}\}}^{\frac{1}{4}}} =______

(a)	$\frac{4}{3} {(\frac{x - 1}{x + 2})}^{\frac{1}{4}} + c$
(b)	$\frac{4}{3} {(\frac{x + 2}{x - 1})}^{\frac{1}{4}} + c$
(c)	$\frac{1}{3} {(\frac{x - 1}{x + 2})}^{\frac{1}{4}} + c$
(d)	$\frac{1}{3} {(\frac{x + 2}{x - 1})}^{\frac{1}{4}} + c$

174.

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

(a)	$\log \|\sin θ - \cos θ + \sqrt{\sin 2 θ}\| + c$
(b)	$\sin^{- 1} (\sin θ - \cos θ) + c$
(c)	$\sin^{- 1} (\sin θ + \cos θ) + c$
(d)	$\sin^{- 1} (\sin θ - \sin θ) + c$

175.

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

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

176.

\int e^{x} \sin x dx

= _____ + c

(a)	e^x (sin x + cos x)
(b)	$\frac{e^{x}}{\sqrt{2}} (\sin x - \cos x)$
(c)	$\frac{e^{x}}{\sqrt{2}} \sin (x - \frac{π}{4})$
(d)	$\frac{e^{x}}{\sqrt{2}} \sin (x + \frac{π}{4})$

177.

\int e^{x} (\frac{1 + x \log x}{x}) dx

= _____ + c

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

178.

\int \tan^{- 1} x dx

= _____ +c

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

179.

\int e^{4 x} (\frac{1 - \sin 4 x}{1 - \cos 4 x}) d x

= _____ + c

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

180.

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

= _____ + c

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

Showing 171 to 180 out of 440 Questions