Originally Posted by

**pghaffari** Hi guys,

i'm currently learning substitution in definite integrals and one part of this chapter is finding the area between two curves.. however for this one problem i keep getting 0 as the area which i am not sure if it is right or not

heres the problem

basically, find the areas of the shaded region

(i can't draw it so i'll just inform you of the upper and lower curves)

f(x) = y=1

g(x) = y = (cosx)^2

First step i did was i found the limits of integration. To do this I solved y = 1 and y = (cosx)^2 simultaneously for x getting...

(cosx)^2 = 1

Hence, x = 0,pie making a = 0 and b = pie

then I integrate...

{ (b,a) (f(x)-g(x))dx

=

{ (pie,0) (1- (cosx)^2)dx

or

{ (pie,0) (sinx)^2 dx

u = sinx, du = dx (HOW?)

{ 0,0 u^2 du

which EQUALS 0....

Is that right? I dont think the AREA is 0 though....what's wrong?

Thanks in advance