Area between Two Sine Curves on [0,pi/2]

[Momentum09]

Homework Statement

Compute the area between the graphs of f(x) = 8sin(2x) and g(x) = 5sin(x)+3sin(2x) on the interval [0,pi/2]

Homework Equations

Area = Integral of [f(x)-g(x)]dx

The Attempt at a Solution

I first did f(x) - g(x) = 5sin(2x)-5sin(x)...after integrating, I got -5/2cos(2x)+5cos(x). Using pi/2 as the upper bound and 0 as the lower bound, I did the calculations but the answer wasn't right. Could someone please point out where I made a mistake?
Thank you very much!

 

[jhicks]

Ask yourself: do the two functions cross at all?

 

[Defennder]

Ask yourself: do the two functions cross at all?

They do intersect at x=0, but nowhere else in that interval. It doesn't matter if it doesn't cross, since all you need to do is to find area in between the two curves, and not necessarily between two points where they intersect.

 

[jhicks]

According to my TI-89 there's a place where they cross on the interval in question. If you presumed that f(x)-g(x) was always positive on that interval (which it appears the OP did) then at some point the areas would start to subtract from the total, which is wrong because there's no such thing as "negative" area between two curves.

 

[Defennder]

Well actually I misread the graph. They do indeed cross somewhere else at (0,pi/2). So the OP must identify the intersection and split the integral into two intervals to evaluate.