1.

Find the area of the region bounded by the curve ` y = sinx `, the lines ` x = - ( pi ) /(2), x = ( pi ) /(2) ` and X- axis.

Answer» Required Area `=int_(-pi//2)^(pi//2)y.dx,` where `y=sinx`
`=int_(-pi//2)^(pi//2)sinx dx`
`=2int_(0)^(pi//2)sinx.dx" (Using property)"`
`=2[-cosx]_(0)^(pi//2)`
`=2[-cos pi//2+cos0]`
`=2[0+1]="2 sq. units."`


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