1
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$I_n=\int\left(\cos ^n x+\sin ^n x\right) d x$$ and $$I_n-\frac{n-1}{n} I_{n-2} =\frac{\sin x \cos x}{n} f(x)$$, then $$f(x)=$$

A
$$\cos ^{n-2} x+\sin ^{n-2} x$$
B
$$\cos ^{n-2} x-\sin ^{n-2} x$$
C
$$\frac{\cos ^{n-2} x-\sin ^{n-2} x}{n}$$
D
$$\frac{\cos ^{n-2} x+\sin ^{n-2} x}{n}$$
2
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$f(x)=\int x^2 \cos ^2 x\left(2 x \tan ^2 x-2 x-6 \tan x\right) d x$$ and $$f(0)=\pi$$, then $$f(x)=$$

A
$$x^2 \sin x+\pi$$
B
$$\cos x+\pi-1$$
C
$$-x^3 \sin 2 x+\pi$$
D
$$x^3 \cos 2 x+\pi \cos x$$
3
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$\int \frac{e^{\sqrt{x}}}{\sqrt{x}}(x+\sqrt{x}) d x=e^{\sqrt{x}}[A x+B \sqrt{x}+C]+K$$ then $$A+B+C=$$

A
$$-$$2
B
2
C
4
D
$$-$$4
4
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$\int \frac{1+\sqrt{\tan x}}{\sin 2 x} d x=A \log \tan x+B \tan x+C$$, then $$4 A-2 B=$$

A
$$-$$1
B
2
C
1
D
$$-$$2
AP EAPCET Subjects
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