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1
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_0^{\pi / 2} \frac{\sin x}{1+\cos x+\sin x} d x= $$

A

$\frac{\pi}{2}+\frac{1}{2} \log 2$

B

$\frac{\pi}{4}-\frac{1}{2} \log 2$

C

$\frac{\pi}{4}$

D

$\frac{3 \pi}{4}+\log 2$

2
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_0^\pi \frac{x \sin x}{1+\cos ^2 x} d x= $$

A

$\frac{\pi^2}{4}$

B

$\frac{\pi}{2}$

C

$\frac{\pi^2}{2}$

D

$\frac{\pi}{4}$

3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\int_0^{2 \pi}\left(\sin ^4 x+\cos ^4 x\right) d x=K \int_0^\pi \sin ^2 x d x+L \int_0^{\frac{\pi}{2}} \cos ^2 x d x$ and $K, L \in N$, then the number of possible ordered pairs ( $K, L$ ) is

A
1
B
2
C
3
D
4
4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int_0^\pi \frac{x \sin x}{4 \cos ^2 x+3 \sin ^2 x} d x$ is equal to
A
$\frac{\pi^2}{6 \sqrt{3}}$
B
$\frac{\pi}{3 \sqrt{3}}$
C
$\frac{\pi^2}{3 \sqrt{3}}$
D
$\sqrt{3} \pi^2$
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