MCQs of સંકલન

Showing 201 to 210 out of 428 Questions

201.

\int \sqrt{3 - x^{2}} d x

= _____+ c (જયાં

|x| < \sqrt{3}

)

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

202.

\int e^{x} (1 + \tan x + \tan^{2} x) dx

= _____ + c

203.

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

= _____ + c

204.

\int x \cos 2 x dx

= _____ + c

205.

જો

\int f (x) d x ψ (x)

, તો

\int x^{5} f (x^{3}) d x

= _____ .

206.

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

= _____

207.

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

= _____ .

208.

\int e^{x} (1 - \cot x + \cot^{2} x) d x

= _____

209.

જો

f (x) = \frac{\sin^{- 1} x}{\sqrt{1 - x^{2}}}

અને

g (x) = e^{\sin^{- 1} x}

હોય તો,

\int f (x) g (x) d x

= _____

210.

\int e^{\sin θ} (\log \sin θ + {cosec}^{2} θ) \cos θ d θ

= _____ .

Showing 201 to 210 out of 428 Questions