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.`

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

What is the area under the curve f(x) = xe^(x) above the x -axis and between thelines x = 0 and x = 1 ?

What is the area under the curve f(x)=xe^(x) above the X-axis and between the lines x=0 and x=1?

The area under the curve y+sqrt(3) sin x=sin 2x between the ordinates x=0 and x=(pi)/6 is

Area under the curve y = x sin x^(2) , bounded by the lines x = 0 and x= sqrt(pi//2) is

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) . .

Find the area bounded by the curve f(x)=x+ sin x and its inverse function between the ordinates x=0" to "x=2pi .

Calculate the area bounded by the curve: f (x)= sin ^(2) "" (x)/(2), axis of x and the ordinates: x =0, x = (pi)/(2).

Find the area bounded by the curve f(x)= maximum {1+sin x,1,1-cos x} and the x - axis between the ordinates x=-pi and x=pi

If the total area between the curves f(x)=cos^(-1)(sin x) and g(x)=sin^(-1)(cos x) on the interval [-7 pi,7 pi] is A,then find the value of 49A