1
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
$\int\limits_0^{\frac{\pi}{2}} \log \left(\frac{5+4 \sin x}{5+4 \cos x}\right) d x=$
A
0
B
2
C
$-$2
D
$\frac{3}{4}$
2
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int_0^\pi \frac{e^{\cos x}}{e^{\cos x}+e^{-\cos x}} d x$ is equal to
A
$\pi$
B
$2 \pi$
C
$\frac{\pi}{4}$
D
$\frac{\pi}{2}$
3
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { The value of the integral } \int_\limits{\frac{1}{3}}^1 \frac{\left(x-x^3\right)^{\frac{1}{3}}}{x^4} d x \text { is } $$

A
4
B
0
C
3
D
6
4
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$a$$ is a real number such that $$\int_\limits0^a x d x \leq a+4$$ then

A
$$ -2 \leq a \leq 0 $$
B
$$ 0 \leq a \leq 4 $$
C
$$ -2 \leq a \leq 4 $$
D
$$ a \leq-2 \text { or } a \geq 4 $$
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