1
JEE Main 2024 (Online) 4th April Morning Shift
+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
+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
+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
+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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