1
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$I_n=\int_0^{\pi / 4} \tan ^n x d x$$, then $$\frac{1}{I_2+I_4}+\frac{1}{I_3+I_5}+\frac{1}{I_4+I_6}=$$

A
$$\frac{1}{I_9+I_{11}}$$
B
$$\frac{1}{I_{10}+I_{12}}$$
C
$$\frac{1}{I_{12}+I_{14}}$$
D
$$\frac{1}{I_{11}+I_{13}}$$
2
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$\int_0^{\pi / 4} e^{\tan ^2 \theta} \sin ^2 \theta \tan \theta d \theta=$$

A
$$\frac{1}{2}\left(\frac{e}{2}-1\right)$$
B
$$\frac{e}{2}-1$$
C
$$\frac{\pi}{2}$$
D
$$2\left(\frac{\pi}{2}-e\right)$$
3
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$\int_{\pi / 4}^{5 \pi / 4}(|\cos t| \sin t+|\sin t| \cos t) d t=$$

A
0
B
1
C
1/2
D
$$\sqrt3/2$$
4
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$f(x)=\max \{\sin x, \cos x\}$$ and $$g(x)=\min \{\sin x, \cos x\}$$, then $$\int_0^\pi f(x) d x+\int_0^\pi g(x) d x=$$

A
$$2 \sqrt{2}+2$$
B
$$2 \sqrt{2}-2$$
C
2
D
$$2 \sqrt{2}$$
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