1
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } I_n=\int_\limits0^{\frac{\pi}{4}} \tan ^n x d x \text {, for } n \geq 2 \text {, then } I_n+I_{n-2}= $$

A
$$\frac{1}{n-1}$$
B
$$\frac{1}{n+1}$$
C
$$\frac{1}{n}+\frac{1}{n-2}$$
D
$$\frac{1}{n}$$
2
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_\limits{-1}^1 \frac{d}{d x}\left(\tan ^{-1} \frac{1}{x}\right) d x \text { is } $$

A
$$ \frac{\pi}{4} $$
B
$$ -\frac{\pi}{2} $$
C
$$ -\frac{\pi}{4} $$
D
$$ \frac{\pi}{2} $$
3
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\int\limits_{-\pi / 2}^{\pi / 2} \sin ^2 x d x$$ is equal to

A
0
B
$$\pi$$
C
$$\frac{\pi}{2}$$
D
$$\frac{\pi}{4}$$
4
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_0^2\left|x^2+2 x-3\right| d x \text { is equal to } $$

A
3
B
6
C
2
D
4
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