1
AP EAPCET 2021 - 20th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\int \frac{\sin \alpha}{\sqrt{1+\cos \alpha}} d \alpha$$ is equal to

A
$$-2 \sqrt{2} \cos \left(\frac{\alpha}{2}\right)+C$$
B
$$2 \sqrt{2} \cos \left(\frac{\alpha}{2}\right)+C$$
C
$$\sqrt{2} \cos \left(\frac{\alpha}{2}\right)+C$$
D
$$-\sqrt{2} \cos \left(\frac{\alpha}{2}\right)+C$$
2
AP EAPCET 2021 - 20th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$\int \frac{\cos 4 x+1}{\cot x-\tan x}=k \cos 4 x+C$$, then $$k$$ is equal to

A
$$\frac{-1}{2}$$
B
$$\frac{-1}{8}$$
C
$$\frac{-1}{3}$$
D
$$\frac{-1}{5}$$
3
AP EAPCET 2021 - 20th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$\int\left[\cos (x) \cdot \frac{d}{d x}(\operatorname{cosec}(x)] d x=f(x)+g(x)+c\right.$$ then $$f(x) \cdot g(x)$$ is equal to

A
$$x \cot (x)$$
B
$$x \tan (x)$$
C
$$x \cos (x)$$
D
1
4
AP EAPCET 2021 - 20th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$\int \frac{(2 x+1)^6}{(3 x+2)^8} d x=P\left(\frac{2 x+1}{3 x+2}\right)^Q+R$$, then $$\frac{P}{Q}$$ is equal to

A
$$\frac{1}{7^2}$$
B
$$\frac{1}{7}$$
C
$$7^2$$
D
7
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