1
AP EAPCET 2022 - 4th July Evening Shift
+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
$$2\left(\frac{\pi}{2}-e\right)$$
2
AP EAPCET 2022 - 4th July Evening Shift
+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
$$\sqrt3/2$$
3
AP EAPCET 2022 - 4th July Evening Shift
+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
$$2 \sqrt{2}$$
4
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

$$\int_0^1 a^k x^k d x=$$

A
$$\lim _\limits{n \rightarrow \infty} \frac{a^k\left(1+2^k+3^k \ldots+n^k\right)}{n^{k+1}}$$
B
$$\lim _\limits{n \rightarrow \infty} \frac{a^k+a^k+\ldots+a^k}{n^{k+1}}$$
C
$$\lim _\limits{n \rightarrow \infty} \frac{1}{n} \Sigma\left(\frac{r}{n}\right)^k$$
D
$$\lim _\limits{n \rightarrow \infty} \frac{1}{n} \Sigma\left(\frac{2 r}{n}\right)^k$$
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