Find the area between y=4sinx and y=10cosx over the interval [0,π]. sketch the curves if necessary.

for all , while for and for . So you already know that over the second half of the interval.

In the first half, is an increasing function, from to . Meanwhile is a decreasing function, from to . Therefore there must be a point between 0 and where the two curves intersect. So we find it:



So we know that in , and in .

The area between the curves is then

The coordinates of point a right now is (-3,-1) you have to multiply these coordinates by a factor of 2 to get (-6,-2)