Question

Can anyone please solve urgently? ​

Answer 1

Question :

$\tt \displaystyle \int \limits_{-4}^{-1} \frac{\pi}{2} d\theta$ = ?

Solution :

$\tt \displaystyle \int \limits_{-4}^{-1} \frac{\pi}{2} d\theta$

$\tt \implies \frac{\pi}{2} \displaystyle \int\limits_{-4}^{-1} d\theta$

$\tt \implies \frac{\pi}{2} \theta$

$\tt \implies \frac{-1\pi}{2} - \frac{-4\pi}{2}$

$\tt \implies - \frac{\pi}{2} + 2\pi$

$\tt \implies \frac{3\pi}{2}$

$\tt \displaystyle \int \limits_{-4}^{-1} \frac{\pi}{2} d\theta =\frac{3\pi}{2}$

Formulas of integration :

● $\tt \int {x}^{n} \: dx = \frac{{x}^{n+1}}{n+1} + c$

● $\tt \int {e}^{x} \: dx = {e}^{x} + c$

● $\tt \int \frac{1}{x}\: dx = logx + c$

● $\tt \int sinx \: dx = -cosx + c$

● $\tt \int cosx\:dx = sinx + c$

● $\tt \int {sec}^{2} x \:dx = tanx + c$

● $\tt \int {cosec}^{2}x \:dx = - cotx + c$

● $\tt \int secxtanx \: dx = secx + c$

● $\tt \int cosecx.cotx \:dx = cosec x + c$