1
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\text { If } \int e^{x^2} \cdot x^3 \mathrm{~d} x=e^{x^2} \cdot[f(x)+C]$$ (where $$C$$ is a constant of integration.) and $$f(1)=0$$, then value of $$f(2)$$ will be

A
$$\frac{-3}{2}$$
B
$$\frac{-1}{2}$$
C
$$\frac{3}{2}$$
D
$$\frac{1}{2}$$
2
MHT CET 2021 24th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int e^x\left(\frac{1+\sin x}{1+\cos x}\right) d x=$$

A
$$e^x \tan \frac{x}{2}+c$$
B
$$e^x \cot \frac{x}{2}+c$$
C
$$e^x \cos \frac{x}{2}+c$$
D
$$e^x \sin \frac{x}{2}+c$$
3
MHT CET 2021 24th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \cos ^3 x e^{\log (\sin x)^2} d x=$$

A
$$ \frac{\sin ^3 x}{3}-\sin ^5 x+c $$
B
$$ \frac{\sin ^3 x}{3}-\frac{\sin ^5 x}{5}+c $$
C
$$ \frac{\sin ^3 x}{3}+\frac{\sin ^5 x}{5}+c $$
D
$$ \sin ^3 x+\sin ^5 x+c $$
4
MHT CET 2021 24th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{d x}{e^x+e^{-x}+2}=$$

A
$$\frac{1}{\mathrm{e}^{2 \mathrm{x}}+1}+\mathrm{c}$$
B
$$\frac{-1}{\mathrm{e}^{\mathrm{x}}+1}+\mathrm{c}$$
C
$$\frac{1}{e^x}+c$$
D
$$\frac{-1}{e^x}+c$$
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