MCQs of Integrals

Showing 71 to 80 out of 421 Questions

71.

\int \frac{c o s^{4} x}{s i n^{2} x}

dx = px + qsin 2x + r cot x + c, then

72.

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

73.

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

74.

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

75.

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

76.

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

77.

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

78.

\int_{1}^{k} f (x) d x = 47, f (x) = \{\begin{cases} 2 x + 8 & 1 \leq x \leq 2 \\ 6 x & 2 < x \leq k \end{cases}

, then k = _____ .

79.

if \int f (x) d x = \frac{{(l o g x)}^{4}}{4} + c, then f (x) =_____

80.

\int \sqrt{1 + c o s x} d x =_____+ c, π < x < 2 π

Showing 71 to 80 out of 421 Questions