Calculate the area of the region enclosed by the x-axis and one arch of the curve y = sin x.

y = sinx. To find the area under the curve and x axis for
one arc of the function.

We know that sinx  has an arc   y
= sinx above axis for x in (0 , pi).

So the area A under
the arc of the curve y = sinx is got by integrating y = sinx fro x = 0 to x=
pi.

A = Integral sinx dx from x = 0 to x =
pi.

A= {(-cosx) at x= pi}- {-cosx)at x=
0}

A ={ - (-1) - (-1)} , as cos 0 = 1 and cos(pi) =
-1

A= 1+1

A =
2.

Therefore the area undeer the curve y = sinx and x axis 
in the interval (0,pi) is 2.