1
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
$$\lim _\limits{n \rightarrow \infty} \frac{1}{n} \Sigma\left(\frac{2 r}{n}\right)^k$$
2
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

Let $$\alpha$$ and $$\beta(\alpha<\beta)$$ are roots of $$18 x^2-9 \pi x+\pi^2=0, f(x)=x^2, g(x)=\cos x$$. Then, $$\int_\alpha^\beta x(g \circ f(x)) d x=$$

A
$$\frac{\sqrt{3}-1}{4}$$
B
$$\frac{\sqrt{3}}{4}$$
C
$$\frac{2+\sqrt{3}}{2}$$
D
$$\frac{1}{2}\left(\sin \frac{\pi^2}{9}-\sin \frac{\pi^2}{36}\right)$$
3
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

$$\int_0^\pi x\left(\sin ^2(\sin x)+\cos ^2(\cos x)\right) d x=$$

A
$$\pi^2$$
B
$$\pi^2 / 2$$
C
$$2 \pi$$
D
$$\pi / 4$$
4
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

If $$\int_0^a {{{dx} \over {4 + {x^2}}} = {\pi \over 8}}$$, then the value of a is equal to

A
1
B
2
C
3
D
4
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