Compare the areas under the curves `y=cos ^2 x and y= sin ^2`x between x=0 and `x=pi `

Show that the areas under the curves f (x) = cos ^(2) x and f (x) = sin ^(2) x between x =0 and x = pi are 1:1.

The area bounded by the curves y=cos x and y=sin x between the ordinates x=0 and x=(3 pi)/(2) is

Find the area enclosed the curve y=sin x and the X-axis between x=0 and x=pi .

In the adjacent figure the graph of two function y=f(x) and y=sin x are given y=sin x intersects, y=f(x) at A(a,f(a)), B(pi,0) and C(2pi,0) . A_(i)(i=1,2,3) is the area bounded by the curves y=f(x) and y=sin x between x=0 and x=a,i=1 between x=a and x=pi, i=2 between x=pi and x=2pi,i=3 . If A_(1)=1-sin a+(a-1) cos a, determine the function f(x). Hence, determine a and A_(1) . Also, calculate A_(2) and A_(3) . .

The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and x = (3pi)/(2) , is