1
TG EAPCET 2025 (Online) 4th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\int x^3 \sin 3 x d x=\frac{1}{27}[f(x) \cos 3 x+g(x) \sin 3 x]+C$, then $f(\mathrm{l})+g(\mathrm{l})=$

A

14

B

6

C

4

D

12

2
TG EAPCET 2025 (Online) 4th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $I_1=\int \sin ^6 x d x$ and $I_2=\int \cos ^6 x d x$, then $I_1+I_2=$

A

$\frac{5 x}{8}+\frac{3 \cos 4 x}{32}+C$

B

$\frac{1}{32}(20 x-3 \sin 4 x)+C$

C

$\frac{1}{32}(20 x+3 \sin 4 x)+C$

D

$\frac{5 x}{4}+\frac{3 \sin 4 x}{16}+C$

3
TG EAPCET 2025 (Online) 4th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{x+\cos x}{1-\sin x} d x= $$

A

$x \tan \left(\frac{\pi}{4}+\frac{x}{2}\right)+C$

B

$x \tan \frac{x}{2}+C$

C

$x \cot \frac{x}{2}+C$

D

$x \cot \left(\frac{\pi}{4}+\frac{x}{2}\right)+C$

4
TG EAPCET 2025 (Online) 4th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\int \frac{1}{(x+2) \sqrt{x^2+x+2}} d x=$

A

$-\frac{1}{2} \sinh ^{-1}\left(\frac{2-3 x}{\sqrt{7}(x+2)}\right)+C$

B

$-\frac{1}{2} \sin ^{-1}\left(\frac{2+3 x}{\sqrt{7}(x+2)}\right)+C$

C

$\frac{1}{2} \cosh ^{-1}\left(\frac{2+3 x}{\sqrt{7}(x+2)}\right)+C$

D

$-\frac{1}{2} \cos ^{-1}\left(\frac{2-3 x}{\sqrt{7}(x+2)}\right)+C$

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