Question

lets solve this integral calculus together!! help me to solve this! it'll b a great help fr me!! ^_^​

Answer 1

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

To prove:-

$\bigstar\sf{\blue{\:\int \limits _{ 0}^{\frac{\pi}{2}} (\sin x+\cos x)dx}}$

$\Large{\underline{\underline{\mathfrak{\bf{Prove}}}}}$

$:\mapsto\sf{\red{\:\int \limits _{ 0}^{\frac{\pi}{2}} (\sin x+\cos x)dx}} \\ \\ \\ \small\sf{\green{\:\star\int \sin x dx \:=\:-\cos x\:\:and\:\:\int \cos x \:=\:\sin x}} \\ \\ \\ :\mapsto\sf{\:\big[(-\cos x+\sin x)\big]_{0}^{\frac{\pi}{2}}} \\ \\ \\ \small\sf{\green{\:\star\cos \frac{\pi}{2}\:=\:0\:\:and\:\:\sin \frac{\pi}{2}\:=\:1}} \\ \\ \\ \small\sf{\green{\:\star\cos 0\:=\:1\:\:and\:\:\sin 0\:=\:0}} \\ \\ \\ :\mapsto\sf{\:(-\cos \dfrac{\pi}{2}+\sin \dfrac{\pi}{2}+\cos 0-\sin 0)} \\ \\ \\ :\mapsto\sf{\:(-0+1+1-0)} \\ \\ \\ :\mapsto\sf{\orange{\:2\:\:\:\:\:Ans.}}$

Answer 2

Answer:

2 is answer of question