MCQs of સંકલન

Showing 71 to 80 out of 440 Questions

71.

\int \sqrt{\frac{a - x}{a + x}} d x =____+ c

72.

જો

\int \frac{c o s^{4} x}{s i n^{2} x} d x = p x + q s i n 2 x + r c o t x + c,

તો

73.

\int \frac{e^{x}}{e^{2 x} e^{x} + 1} d x =_____+ c

74.

\int \frac{1}{\sqrt{2 - 3 x - x^{2}}} d x =_____+ c

75.

\int \frac{x^{2} + 1}{x^{4} - x^{2} + 1} d x =_____+ c

76.

\int (\sqrt{t a n x} + \sqrt{c o t x}) d x =_____+ c

(a)	$\frac{t a n x}{\sqrt{2}} t a n^{- 1} (\frac{c o t x + 1}{\sqrt{2 t a n x}})$
(b)	$\sqrt{2} t a n^{- 1} (\frac{t a n x - 1}{\sqrt{2 t a n x}})$
(c)	$\sqrt{2} t a n^{- 1} (\frac{t a n x + 1}{\sqrt{2 t a n x}})$
(d)	$\frac{t a n x}{\sqrt{2}} t a n^{- 1} (\frac{c o t x + 1}{\sqrt{2 t a n x}})$

77.

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

(a)	$2 \log (\frac{\sqrt{1 + x} - 1}{\sqrt{1 + x} + 1}) - 2 s i n^{- 1} \sqrt{x}$
(b)	$\log (\frac{\sqrt{1 - x} - 1}{\sqrt{1 + x} + 1}) + 2 s i n^{- 1} (\frac{\sqrt{1 - x}}{\sqrt{1 + x}})$
(c)	$\log (\frac{1 - \sqrt{1 - x}}{1 + \sqrt{1 - x}}) + \frac{1}{2} c o t^{- 1} \sqrt{x + 1}$
(d)	$\log (\frac{\sqrt{1 - x} - 1}{\sqrt{1 - x} + 1}) - 2 s i n^{- 1} \sqrt{x}$

78.

\int \frac{d x}{{(9 - x^{2})}^{\frac{3}{2}}} =_____+ c

79.

જો

\int x^{3} \sqrt{\frac{1 + x^{2}}{1 - x^{2}}} d x = p c o s^{- 1} x^{2} + q \sqrt{1 - x^{4}} + r x^{2} \sqrt{1 - x^{4}} + c,

તો

p + q + r =_____

80.

જો

\int \sqrt{1 + \sin x} . f (x) . d x = \frac{2}{3} (1 + \sin x)^{\frac{3}{2}} + c

હોય તો f (x) = _____

Showing 71 to 80 out of 440 Questions