MCQs of સંકલન

Showing 401 to 410 out of 428 Questions

401.

\int_{\frac{π}{6}}^{\frac{π}{3}} \frac{d x}{\sin 2 x} =_____

402.

I_{n} = \int c o t^{n} x d x

હોય તો,

I_{0} + I_{1} + 2 (I_{2} + I_{3}) + I_{4} + I_{5} =_____

(જ્યાં u=cot x)

403.

\int \frac{f (x)}{x^{3} - 1} d x =_____+ c

જ્યાં f(x) ચલ x માં દ્વિઘાત બહુપદી છે. f(0)=f(1)=-3 તથા f(2)=-1

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

404.

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

405.

\int \{\cos^{- 1} x + \cos^{- 1} \sqrt{1 - x^{2}}\} d x, \forall x \in [- 1, 0] =_____+ c

406.

\int \frac{d x}{(x^{2} + 1) (x^{2} + 4)} = A \tan^{- 1} x + B \tan^{- 1} \frac{x}{2} + c

હોય તો,

A + B =_____

407.

\int \sqrt{x^{2} - 8 x + 7} d x =_____+ c

(a)	$\frac{1}{2} (x - 4) \sqrt{x^{2} - 8 x + 7} + 9 \log \|x - 4 + \sqrt{x^{2} - 8 x + 7}\|$
(b)	$\frac{1}{2} (x + 4) \sqrt{x^{2} - 8 x + 7} + 9 \log \|x + 4 + \sqrt{x^{2} - 8 x + 7}\|$
(c)	$\frac{1}{2} (x - 4) \sqrt{x^{2} - 8 x + 7} - 3 \sqrt{2} \log \|x - 4 + \sqrt{x^{2} - 8 x + 7}\|$
(d)	$\frac{1}{2} (x - 4) \sqrt{x^{2} - 8 x + 7} - \frac{9}{2} \log \|x - 4 + \sqrt{x^{2} - 8 x + 7}\|$

408.

\int x^{2 n - 1} \sin x^{n} d x =_____+ c

409.

\int \frac{x e^{x}}{\sqrt{1 + e^{x}}} d x = f (x) \sqrt{1 + e^{x}} - 2 \log |\frac{\sqrt{1 + e^{x}} - 1}{\sqrt{1 + e^{x}} + 1}| + c

તો

f (x) =_____

410.

\int_{0}^{\frac{π}{2}} \frac{dx}{1 + sinx} =_____

Showing 401 to 410 out of 428 Questions