MCQs of સંકલન

Showing 191 to 200 out of 428 Questions

191.

\int e^{\frac{x}{\sqrt{2}}} \cos (\frac{x}{\sqrt{2}}) dx

= _____ + c

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

192.

\int (1 + x)^{2} e^{x} dx = e^{x} (____) + c

193.

\int \frac{1 + \tan x}{e^{- x} \cos x} dx

= _____ + c

194.

\int \frac{x + \sin x}{1 + \cos x}

dx = _____ + c

195.

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

= _____ + c

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

196.

\int \sin^{- 1} x dx

= _____ + c

197.

જો

\int x \cdot e^{2 x} dx = e^{2 x} f (x) + c

, જયાં c સ્વૈર અચળ છે તો f(x) = _____ .

198.

\int (1 - \cos x) {cosec}^{2} x dx

= _____ + c

199.

\int e^{7 x + \log x} dx

= _____ + c

200.

\int e^{x} cosec x (1 - \cot x) dx

= _____ + c

Showing 191 to 200 out of 428 Questions