1
KCET 2025
MCQ (Single Correct Answer)
+1
-0

The value of $\int_{-1}^1 \sin ^5 \mathrm{x} \cos ^4 \mathrm{xdx}$ is

A
$-\pi / 2$
B
$\pi$
C
$\pi / 2$
D
0
2
KCET 2025
MCQ (Single Correct Answer)
+1
-0

$$ \text { The value of } \int_0^{2 \pi} \sqrt{1+\sin \left(\frac{x}{2}\right)} d x \text { is } $$

A
8
B
4
C
2
D
2
3
KCET 2025
MCQ (Single Correct Answer)
+1
-0
$\int \frac{\mathrm{dx}}{\mathrm{x}^2\left(\mathrm{x}^4+1\right)^{3 / 4}}$ equals
A
$\left(\frac{x^4+1}{x^4}\right)^{\frac{1}{4}}+c$
B
$\left(x^4+1\right)^{\frac{1}{4}}+c$
C
$-\left(\mathrm{x}^4+1\right)^{\frac{1}{4}}+\mathrm{c}$
D
$-\left(\frac{x^4+1}{x^4}\right)^{\frac{1}{4}}+c$
4
KCET 2025
MCQ (Single Correct Answer)
+1
-0

$\int_0^1 \log \left(\frac{1}{x}-1\right) d x$ is

A
1
B
0
C
$\log _{\mathrm{e}} 2$
D
$\log _{\mathrm{e}}\left(\frac{1}{2}\right)$
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