Indefinite Integrals
111 Questions
1994
JEE Advanced
Numerical
IIT-JEE 1994
Find the indefinite integral $\,\int {\cos 2\theta {\mkern 1mu} ln\left( {{{\cos \theta + \sin \theta } \over {\cos \theta - \sin \theta }}} \right)} {\mkern 1mu} d\theta $
Correct Answer: $$\,\,{{\sin 2\theta } \over 2}\,ln\left( {{{\cos \theta + \sin \theta } \over {\cos \theta - \sin \theta }}} \right)$$ $$ - {1 \over 2}l$$$$n\sec 2\theta + C$$
1992
JEE Advanced
Numerical
IIT-JEE 1992
Find the indefinite integral $\int {\left( {{1 \over {\root 3 \of x + \root 4 \of 4 }} + {{In\left( {1 + \root 6 \of x } \right)} \over {\root 3 \of x + \root \, \of x }}} \right)} dx$
Correct Answer: Solve it.
1990
JEE Advanced
Numerical
IIT-JEE 1990
If $\int {{{4{e^x} + 6{e^{ - x}}} \over {9{e^x} - 4{e^{ - x}}}}\,dx = Ax + B\,\,\log \left( {9{e^{2x}} - 4} \right) + C,} $ then
$A = .....,B = .....$ and $C = .....$
$A = .....,B = .....$ and $C = .....$
Correct Answer: $$ - {3 \over 2},{{35} \over {36}},$$ any real value
1989
JEE Advanced
Numerical
IIT-JEE 1989
Evaluate $\int {\left( {\sqrt {\tan x} + \sqrt {\cot x} } \right)dx} $
Correct Answer: $$\sqrt 2 {\tan ^{ - 1}}\left( {{{\sqrt {\tan x} - \sqrt {\cot x} } \over {\sqrt 2 }}} \right) + C$$
1987
JEE Advanced
Numerical
IIT-JEE 1987
Evaluate :$\,\,\int {\left[ {{{{{\left( {\cos 2x} \right)}^{1/2}}} \over {\sin x}}} \right]dx} $
Correct Answer: $${1 \over {\sqrt 2 }}\,\log \left[ {{{\sqrt 2 + \sqrt {1 - {{\tan }^2}x} } \over {\sqrt 2 - \sqrt {1 - {{\tan }^2}x} }}} \right] - \log \left( {\cot x + \sqrt {{{\cot }^2}x - 1} } \right) + C$$
1985
JEE Advanced
Numerical
IIT-JEE 1985
Evaluate the following $\int {\sqrt {{{1 - \sqrt x } \over {1 + \sqrt x }}dx} } $
Correct Answer: $$ - 2\sqrt {1 - x} + {\cos ^{ - 1}}\sqrt x + \sqrt x \sqrt {1 - x} + C$$
1984
JEE Advanced
Numerical
IIT-JEE 1984
Evaluate the following $\int {{{dx} \over {{x^2}{{\left( {{x^4} + 1} \right)}^{3/4}}}}} $
Correct Answer: $$ - {\left( {1 + {1 \over {{x^{ \to 4}}}}} \right)^{{\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 4$}}}} + C$$
1983
JEE Advanced
Numerical
IIT-JEE 1983
Evaluate : $\int {{{\left( {x - 1} \right){e^x}} \over {{{\left( {x + 1} \right)}^3}}}dx} $
Correct Answer: $${{{e^x}} \over {{{\left( {x + 1} \right)}^2}}} + C$$
1981
JEE Advanced
Numerical
IIT-JEE 1981
Evaluate $\int {\left( {{e^{\log x}} + \sin x} \right)\cos x\,\,dx.} $
Correct Answer: $$x\sin x + \cos x - {1 \over 4}\cos 2x + C$$
1979
JEE Advanced
Numerical
IIT-JEE 1979
Evaluate $\int {{{{x^2}dx} \over {{{\left( {a + bx} \right)}^2}}}} $
Correct Answer: $${1 \over {{b^3}}}\left[ {a + bx - 2a\log \left| {a + bx} \right| - {{{a^2}} \over {a + bx}}} \right] + C$$
1978
JEE Advanced
Numerical
IIT-JEE 1978
Evaluate $\int {{{\sin x} \over {\sin x - \cos x}}dx} $
Correct Answer: $${1 \over 2}\log \left| {\sin x - \cos x} \right| + {x \over 2} + C$$