# Quick question on integral calculation

1. Oct 3, 2011

### matts0

1. The problem statement, all variables and given/known data
Hello, I have a question from my textbook on integral calculation. It's
Find f(pi/2) from the following information.
(i) f is positive and continuous.
(ii) the area under the curve y=f(x) from x=0 to x=a is a2+(a/2)*sin(a)+(π/2 )*cosa

So I think the second condition implies
F(a)-F(0) = a2+(a/2)*sin(a)+(π/2 )*cosa (F is the antiderivate of f)
But if I let a=0, I find the lefthand side of the equation will be 0 but the righthand side will be π/2 .
So please someone tell me where I made a mistake which seems to be quite a silly one.

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 3, 2011

### Hammie

Did you calculate the derivative?

3. Oct 3, 2011

### Ray Vickson

Either you copied the question incorrectly or else the book has written an incorrect question. You are right: the two sides are different in the limit a-->0.

RGV