1

JEE Main 2021 (Online) 24th February Morning Shift

MCQ (Single Correct Answer)

+4

-1

If $$\int {{{\cos x - \sin x} \over {\sqrt {8 - \sin 2x} }}} dx = a{\sin ^{ - 1}}\left( {{{\sin x + \cos x} \over b}} \right) + c$$, where c is a constant of integration, then
the ordered pair (a, b) is equal to :

2

JEE Main 2020 (Online) 5th September Evening Slot

MCQ (Single Correct Answer)

+4

-1

If

$$\int {{{\cos \theta } \over {5 + 7\sin \theta - 2{{\cos }^2}\theta }}} d\theta $$ = A$${\log _e}\left| {B\left( \theta \right)} \right| + C$$,

where C is a constant of integration, then $${{{B\left( \theta \right)} \over A}}$$

can be :

$$\int {{{\cos \theta } \over {5 + 7\sin \theta - 2{{\cos }^2}\theta }}} d\theta $$ = A$${\log _e}\left| {B\left( \theta \right)} \right| + C$$,

where C is a constant of integration, then $${{{B\left( \theta \right)} \over A}}$$

can be :

3

JEE Main 2020 (Online) 5th September Morning Slot

MCQ (Single Correct Answer)

+4

-1

If

$$\int {\left( {{e^{2x}} + 2{e^x} - {e^{ - x}} - 1} \right){e^{\left( {{e^x} + {e^{ - x}}} \right)}}dx} $$ = $$g\left( x \right){e^{\left( {{e^x} + {e^{ - x}}} \right)}} + c$$

where c is a constant of integration, then g(0) is equal to :

$$\int {\left( {{e^{2x}} + 2{e^x} - {e^{ - x}} - 1} \right){e^{\left( {{e^x} + {e^{ - x}}} \right)}}dx} $$ = $$g\left( x \right){e^{\left( {{e^x} + {e^{ - x}}} \right)}} + c$$

where c is a constant of integration, then g(0) is equal to :

4

JEE Main 2020 (Online) 4th September Morning Slot

MCQ (Single Correct Answer)

+4

-1

Let $$f\left( x \right) = \int {{{\sqrt x } \over {{{\left( {1 + x} \right)}^2}}}dx\left( {x \ge 0} \right)} $$. Then f(3) – f(1) is eqaul to :

Questions Asked from Indefinite Integrals (MCQ (Single Correct Answer))

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