# Definite Integration · Mathematics · COMEDK

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COMEDK 2024 Evening Shift
$$\text { The value of the integral } \int_\limits{\frac{1}{3}}^1 \frac{\left(x-x^3\right)^{\frac{1}{3}}}{x^4} d x \text { is }$$
COMEDK 2024 Evening Shift
If $$a$$ is a real number such that $$\int_\limits0^a x d x \leq a+4$$ then
COMEDK 2024 Evening Shift
$$\text { If } I_n=\int_\limits0^{\frac{\pi}{4}} \tan ^n x d x \text {, for } n \geq 2 \text {, then } I_n+I_{n-2}=$$
COMEDK 2024 Morning Shift
$$\int_\limits{-1}^1 \frac{d}{d x}\left(\tan ^{-1} \frac{1}{x}\right) d x \text { is }$$
COMEDK 2023 Morning Shift
$$\int\limits_{-\pi / 2}^{\pi / 2} \sin ^2 x d x$$ is equal to
COMEDK 2023 Evening Shift
$$\int_0^2\left|x^2+2 x-3\right| d x \text { is equal to }$$
COMEDK 2022
$$\int\limits_{ - {\pi \over 2}}^{{\pi \over 2}} {\cos x\,dx}$$
COMEDK 2021
$$\int_{ - \pi /2}^{\pi /2} {\sin xdx}$$
COMEDK 2020
The value of the integral $$\int\limits_0^{\pi /2} {({{\sin }^{100}}x - {{\cos }^{100}}x)dx}$$ is
COMEDK 2020
If $$k\int\limits_0^1 {x\,.\,f(3x)dx = \int\limits_0^3 {t\,.\,f(t)dt} }$$, then the value of $$k$$ is
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