1
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$\int \sqrt{e^{4 x}+e^{2 x}} d x$$ is equal to

A
$$\frac{1}{2} e^x\left(\sqrt{e^{2 x}+1}\right)+\frac{1}{2} \sinh ^{-1}\left(e^x\right)+c$$
B
$$\frac{1}{2} e^x\left(\sqrt{e^{2 x}+1}\right)+\sinh ^{-1}\left(e^x\right)+c$$
C
$$\frac{1}{2}\left(\sqrt{e^{2 x}+1}\right)+\frac{1}{2} \sinh ^{-1}\left(e^x\right)+c$$
D
$$\sqrt{e^{4 x}+e^{2 x}}+\sqrt{e^{2 x}+1}+c$$
2
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$\int \frac{1}{1+\sin x} d x=\tan (f(x))+c$$, then $$f^{\prime}(0)$$ is equal to

A
0
B
1
C
$$\frac{1}{2}$$
D
$$\frac{-1}{2}$$
3
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$\int_0^{\pi / 2} \tan ^n(x) d x=k \int_0^{\pi / 2} \cot ^n(x) d x$$, then

A
$$k=1$$
B
$$k=2$$
C
$$k=\frac{1}{2}$$
D
$$k=3$$
4
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$\int_0^2 x e^x d x$$ is equal to

A
$$e^2+1$$
B
$$e^2-1$$
C
$$e^{-1}-1$$
D
$$e^{-1}+1$$
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