1
TG EAPCET 2024 (Online) 10th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\int\left(1+x-x^{-1}\right) e^{\left(x+x^{-1}\right)} d x=f(x)+C$, then $f(1)-f(-1)=$
A
$e^{2}-\frac{1}{e^{2}}$
B
$e^{2}+\frac{1}{e^{2}}$
C
$e+\frac{1}{e}$
D
$e-\frac{1}{e}$
2
TG EAPCET 2024 (Online) 10th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$ \int \frac{1}{x^{m} \sqrt[m]{x^{m}+1}} d x =$
A
$\frac{1}{m-1}\left(\frac{\sqrt[m]{x^{m}+1}}{x}\right)^{m}+C$
B
$\frac{-1}{m-1}\left(\frac{\sqrt[m]{x^{m}+1}}{x}\right)^{m-1}+C$
C
$\frac{-1}{m}\left(\frac{\sqrt[m]{x^{m}+1}}{x}\right)^{m}+C$
D
$\frac{1}{m}\left(\frac{\sqrt[m-1]{x^{m}+1}}{x}\right)^{m}+C$
3
TG EAPCET 2024 (Online) 10th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\int(\sqrt{\operatorname{cosec} x+1}) d x=k \tan ^{-1}(f(x))+C$, then $\frac{1}{k} f\left(\frac{\pi}{6}\right)=$
A
$\frac{1}{2}$
B
$\frac{1}{4}$
C
$-\frac{1}{4}$
D
$-\frac{1}{2}$
4
TG EAPCET 2024 (Online) 10th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$\frac{3}{25} \int_{0}^{25 \pi} \sqrt{\left|\cos x-\cos ^{3} x\right|} d x=$
A
8
B
4
C
1
D
0
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