Definite Integration · Mathematics · COMEDK

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

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

$$\int\limits_{ - {\pi \over 2}}^{{\pi \over 2}} {\cos x\,dx} $$

$$\int_{ - \pi /2}^{\pi /2} {\sin xdx} $$

The value of the integral $$\int\limits_0^{\pi /2} {({{\sin }^{100}}x - {{\cos }^{100}}x)dx} $$ is

If $$k\int\limits_0^1 {x\,.\,f(3x)dx = \int\limits_0^3 {t\,.\,f(t)dt} } $$, then the value of $$k$$ is