question_answer

The area bounded by the curve\[y=sin\text{ }x\] between\[x=0\]and\[x=2\pi \]is (in square units)

A)  1                                            

B)  2    

C)  0                            

D)         4

E)  \[2\pi \]

Correct Answer: D

Solution :

Given curves,\[y=sin\text{ }x,\text{ }x=0\]and\[x=2\pi \] Area of\[OAB=2\]Area of OA (\[\because \]by symmetry)                 \[=2.\int_{x=0}^{\pi }{y\,dx}\]                 \[=2\int_{0}^{\pi }{\sin x\,dx}\]                 \[=-2[\cos x]_{0}^{\pi }\] \[=-2\,(\cos \pi -\cos 0)\]             \[=-2(-1-1)=4\]