Definite Integration · Mathematics · KCET

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MCQ (Single Correct Answer)

1

$\int_{-\pi}^\pi\left(1-x^2\right) \sin x \cdot \cos ^2 x d x$ is

KCET 2024
2

$\int\limits_1^5(|x-3|+|1-x|) d x=$

KCET 2024
3

$$\int\limits_2^8 \frac{5^{\sqrt{10-x}}}{5^{\sqrt{x}}+5^{\sqrt{10-x}}} d x \text { is equals to :}$$

KCET 2023
4

$$\int_{-2}^0\left(x^3+3 x^2+3 x+3+(x+1) \cos (x+1)\right) d x$$ is equals to

KCET 2023
5

$$\int\limits_0^\pi \frac{x \tan x}{\sec x \cdot \operatorname{cosec} x} d x$$ is equals to

KCET 2023
6

If $$[x]$$ is the greatest integer function not greater than $$x$$, then $$\int_\limits0^8[x] d x$$ is equal to

KCET 2022
7

$$\int_0^{\pi / 2} \sqrt{\sin \theta} \cos ^3 \theta d \theta$$ is equal to

KCET 2022
8

$$\int_0^1 \frac{x e^x}{(2+x)^3} d x$$ is equal to

KCET 2022
9

Evaluate $$\int_\limits2^3 x^2 d x$$ as the limit of a sum

KCET 2022
10

$$\int_0^{\pi / 2} \frac{\cos x \sin x}{1+\sin x} d x$$ is equal to

KCET 2022
11

If $$I_n=\int_0^{\frac{\pi}{4}} \tan ^n x d x$$, where $$n$$ is positive integer, then $$I_{10}+I_8$$ is equal to

KCET 2021
12

The value of $$\int_0^{4042} \frac{\sqrt{x} d x}{\sqrt{x}+\sqrt{4042-x}}$$ is equal to

KCET 2021
13

The value of $$\int_{-1 / 2}^{1 / 2} \cos ^{-1} x d x$$ is

KCET 2020
14

Find the value of $$\int_0^1 \frac{\log (1+x)}{1+x^2} d x$$ is

KCET 2020
15

The value of $$\int_{-\pi / 2}^{\pi / 2} \frac{\cos x}{1+e^x} d x$$ is

KCET 2020
16

$$\int_\limits{-3}^3 \cot ^{-1} x d x=$$

KCET 2019
17

$$\int_\limits0^2\left[x^2\right] d x=$$

KCET 2019
18

$$\int_\limits0^1 \sqrt{\frac{1+x}{1-x}} d x=$$

KCET 2019
19
$\int_0^1 \frac{d x}{e^x+e^{-x}}$ is equal to
KCET 2018
20
$ \int_0^{1 / 2} \frac{d x}{\left(1+x^2\right) \sqrt{1-x^2}}$ is equal to
KCET 2018
21
$\int_{-2}^2|x \cos \pi x| d x$ is equal to
KCET 2018
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