Definite Integration · Mathematics · KCET

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MCQ (Single Correct Answer)

1

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

KCET 2025
2

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

KCET 2025
3

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

KCET 2025
4

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

KCET 2024
5

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

KCET 2024
6

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

KCET 2023
7

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

KCET 2023
8

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

KCET 2023
9

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

KCET 2022
10

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

KCET 2022
11

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

KCET 2022
12

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

KCET 2022
13

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

KCET 2022
14

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
15

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

KCET 2021
16

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

KCET 2020
17

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

KCET 2020
18

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

KCET 2020
19

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

KCET 2019
20

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

KCET 2019
21

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

KCET 2019
22
$\int_0^1 \frac{d x}{e^x+e^{-x}}$ is equal to
KCET 2018
23
$ \int_0^{1 / 2} \frac{d x}{\left(1+x^2\right) \sqrt{1-x^2}}$ is equal to
KCET 2018
24
$\int_{-2}^2|x \cos \pi x| d x$ is equal to
KCET 2018
25

$$ \int\limits_{-\pi / 2}^{\pi / 2} \frac{d x}{e^{\sin x}+1} $$

KCET 2017
26
$\int\limits_{-5}^5|x+2| d x$ is equal to
KCET 2017
27

$$ \int\limits_0^{\pi / 2} \frac{1}{a^2 \cdot \sin ^2 x+b^2 \cdot \cos ^2 x} d x $$

KCET 2017
28
$\int\limits_{0.2}^{3.5}[x] d x$ is equal to :
KCET 2017
29
$\int\limits_0^{\pi / 2} \frac{\tan ^7 x}{\cot ^7 x+\tan ^7 x} d x$ is equal to
KCET 2017
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