1

JEE Main 2023 (Online) 25th January Morning Shift

MCQ (Single Correct Answer)

+4

-1

Let $$f(x) = \int {{{2x} \over {({x^2} + 1)({x^2} + 3)}}dx} $$. If $$f(3) = {1 \over 2}({\log _e}5 - {\log _e}6)$$, then $$f(4)$$ is equal to

2

JEE Main 2022 (Online) 29th July Evening Shift

MCQ (Single Correct Answer)

+4

-1

For $$I(x)=\int \frac{\sec ^{2} x-2022}{\sin ^{2022} x} d x$$, if $$I\left(\frac{\pi}{4}\right)=2^{1011}$$, then

3

JEE Main 2022 (Online) 26th July Evening Shift

MCQ (Single Correct Answer)

+4

-1

$$ \text { The integral } \int \frac{\left(1-\frac{1}{\sqrt{3}}\right)(\cos x-\sin x)}{\left(1+\frac{2}{\sqrt{3}} \sin 2 x\right)} d x \text { is equal to } $$

4

JEE Main 2022 (Online) 27th June Morning Shift

MCQ (Single Correct Answer)

+4

-1

If $$\int {{{({x^2} + 1){e^x}} \over {{{(x + 1)}^2}}}dx = f(x){e^x} + C} $$, where C is a constant, then $${{{d^3}f} \over {d{x^3}}}$$ at x = 1 is equal to :

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

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