JEE Main 2024 (Online) 4th April Morning Shift | Definite Integration Question 15 | Mathematics | JEE Main - ExamSIDE.com

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1

JEE Main 2024 (Online) 4th April Morning Shift

MCQ (Single Correct Answer)

+4

-1

$$\text { Let } f(x)=\left\{\begin{array}{lr} -2, & -2 \leq x \leq 0 \\ x-2, & 0< x \leq 2 \end{array} \text { and } \mathrm{h}(x)=f(|x|)+|f(x)| \text {. Then } \int_\limits{-2}^2 \mathrm{~h}(x) \mathrm{d} x\right. \text { is equal to: }$$

A

2

B

6

C

4

D

1

2

JEE Main 2024 (Online) 1st February Evening Shift

MCQ (Single Correct Answer)

+4

-1

If $\int\limits_0^{\frac{\pi}{3}} \cos ^4 x \mathrm{~d} x=\mathrm{a} \pi+\mathrm{b} \sqrt{3}$, where $\mathrm{a}$ and $\mathrm{b}$ are rational numbers, then $9 \mathrm{a}+8 \mathrm{b}$ is equal to :

A

2

B

1

C

3

D

$\frac{3}{2}$

3

JEE Main 2024 (Online) 1st February Evening Shift

MCQ (Single Correct Answer)

+4

-1

The value of $\int\limits_0^1\left(2 x^3-3 x^2-x+1\right)^{\frac{1}{3}} \mathrm{~d} x$ is equal to :

A

-1

B

2

C

0

D

1

4

JEE Main 2024 (Online) 1st February Morning Shift

MCQ (Single Correct Answer)

+4

-1

The value of the integral $\int\limits_0^{\pi / 4} \frac{x \mathrm{~d} x}{\sin ^4(2 x)+\cos ^4(2 x)}$ equals :

A

$\frac{\sqrt{2} \pi^2}{8}$

B

$\frac{\sqrt{2} \pi^2}{16}$

C

$\frac{\sqrt{2} \pi^2}{32}$

D

$\frac{\sqrt{2} \pi^2}{64}$

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