# Homework Help: Evaluating the integral of absolute values

1. Jan 15, 2013

### doctordiddy

1. The problem statement, all variables and given/known data

∫(0 to 3pi/2) -7|sinx|dx

2. Relevant equations

3. The attempt at a solution

I am not sure how to treat it as it has an absolute value

i assumed that you could remove the -7 to get

-7∫|sinx| dx

then integrate sinx into -cosx but since there is absolute value i tried to change -cosx to cosx which ended up as

-7cosx

and then doing -7cos(3pi/2)-(-7cos(0))

but this was incorrect. Can anyone give me any hints?

thanks

2. Jan 15, 2013

### Zondrina

Usually for absolute values you have to break things into cases depending on what values of x you're integrating over.

Notice that from 0 to 3π/2, x≥0? If x≥0, then |sinx| = sinx.

Consider integrating from x=-2 to x=-1, x<0. If x<0, then |sinx| = -sinx.

3. Jan 15, 2013

### CAF123

Sketch the graph of y = sinx from 0 to 3pi/2. From this, can you see what g = |sinx| would look like? Do you then see why integrating sinx to simply -cosx is wrong?

4. Jan 15, 2013

### Staff: Mentor

This is NOT true. If 0 ≤ x ≤ π, then |sinx| = sinx, but for π ≤ x ≤ 2π, sin(x) ≤ 0.
This is not true, either. There are infinitely many intervals for which x < 0 but sin(x) ≥ 0.

5. Jan 15, 2013

### doctordiddy

6. Jan 15, 2013

### CAF123

It is still not right. Can you use |sinx| = sinx if sinx ≥ 0 and |sinx| = -sinx if sinx < 0? This is key to solving the problem.