1
MHT CET 2023 14th May Morning Shift
+2
-0

The integral $$\int_\limits{\frac{\pi}{6}}^{\frac{\pi}{3}} \sec ^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x d x$$ is equal to

A
$$3^{\frac{5}{6}}-3^{\frac{2}{3}}$$
B
$$3^{\frac{7}{6}}-3^{\frac{5}{6}}$$
C
$$3^{\frac{5}{3}}-3^{\frac{1}{3}}$$
D
$$3^{\frac{4}{3}}-3^{\frac{1}{3}}$$
2
MHT CET 2023 13th May Evening Shift
+2
-0

The integral $$\int_\limits{\pi / 6}^{\pi / 3} \sec ^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x d x$$ is equal to

A
$$3^{\frac{5}{6}}-3^{\frac{2}{3}}$$
B
$$3^{\frac{7}{6}}-3^{\frac{5}{6}}$$
C
$$3^{\frac{5}{3}}-3^{\frac{1}{3}}$$
D
$$3^{\frac{4}{3}}-3^{\frac{1}{3}}$$
3
MHT CET 2023 13th May Morning Shift
+2
-0

If $$\mathrm{f}(x)=\left\{\begin{array}{ll}\mathrm{e}^{\cos x} \sin x & , \text { for }|x| \leq 2 \\ 2, & \text { otherwise }\end{array}\right.$$, then $$\int_\limits{-2}^3 \mathrm{f}(x) \mathrm{d} x$$ is equal to

A
0
B
2
C
1
D
3
4
MHT CET 2023 12th May Evening Shift
+2
-0

The value of $$\int_\limits0^\pi\left|\sin x-\frac{2 x}{\pi}\right| \mathrm{d} x$$ is

A
$$\frac{\pi}{4}$$
B
$$\frac{\pi}{2}$$
C
$$\pi$$
D
$$2 \pi$$
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