Question

Find the area between the x-axis and the curve `y=sinx` from `x=0` to `x=2pi`

Answer 1

The graph of `y=sinx` is shown below :

` :. ` Required area
`ar(OABO)+ar(BCDB)`
`=int_(0)^(pi)|sinx|dx+int_(pi)^(2pi)|sinx|dx`
`=int_(0)^(pi)sinx dx+int_(pi)^(2pi)(-sinx)dx`
`=[-cosx]_(0)^(pi)+[cosx]_(pi)^(2pi)`
`= -cos pi+cos0+cos2pi-cos pi`
`=-(-1)+1+1-(-1)`
`=4` sq. units.