1
TS EAMCET 2020 (Online) 11th September Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{x^2}{\left(\sqrt{4-x^2}\right)^3} d x= $$

A

$\frac{x^2}{\sqrt{4-x^2}}-\sin ^{-1}\left(\frac{x}{2}\right)+C$

B

$\frac{x}{\sqrt{4-x^2}}-\tan ^{-1}\left(\frac{x}{\sqrt{4-x^2}}\right)+C$

C

$\frac{x}{\sqrt{4-x^2}}+\sin ^{-1}\left(\frac{2}{\sqrt{4-x^2}}\right)+C$

D

$\sqrt{4-x^2}-\tan ^{-1}\left(\frac{x}{2}\right)+C$

2
TS EAMCET 2020 (Online) 11th September Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{d x}{x \ln (x) \ln ^2(x) \ln ^3(x) \ldots \ln ^m(x)}=\frac{(\ln (x))^K}{K}+C \Rightarrow 2 K= $$

A

$(m+1)(m+2)$

B

$(2-m)(1-m)$

C

$(m+1)(2-m)$

D

$(m+2)(1-m)$

3
TS EAMCET 2020 (Online) 11th September Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $I_m=\int x^m \cos n x d x=g(x)-\frac{m(m-1)}{n^2} I_{m-2}$, then $g(x)=$

A

$\frac{x^m \sin n x}{n}+\frac{m(m-1) x^{m-1} \cos n x}{n^2}$

B

$\frac{x^m \cos n x}{n}+\frac{x^{m-1} m(m-1)}{n^2} \sin n x$

C

$\frac{m}{n} \sin n x+\frac{m}{n^2} x^{m-1} \cos n x$

D

$\frac{x^m \sin n x}{n}+\frac{m}{n^2} x^{m-1} \cos n x$

4
TS EAMCET 2020 (Online) 11th September Evening Shift
MCQ (Single Correct Answer)
+1
-0

Let $I_n=\int \sec ^n x d x$. If $5 I_6-4 I_4=f(x)$, then $f\left(\frac{\pi}{4}\right)$ is equal to

A

2

B

4

C

1

D

$4 / 5$

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