integrals

[jeca86]

evaluate the integral

i dont know how to draw the sign but the 3pi/2 is at the top and the 0 is at the bottom. the rest is absolute value of sinx multiplied by dx.

i got:
cos(3pi/2)-cos0=-1 is this right?

 

[soroban]

Hello, jeca86!

Evaluate the integral: \(\displaystyle \L\,\int^{\;\;\;\frac{3\pi}{2}}_0|\sin x|\,dx\)

I assume you know what the graph of \(\displaystyle y\,=\,sin x\) looks like.

The graph of \(\displaystyle \,y\,=\,|\sin x|\,\) from \(\displaystyle x\,=\,0\,\) to \(\displaystyle \,x\,=\,\frac{3\pi}{2}\,\) looks like this:

      |     ***          **
      |   *:::::*       *:| 
      | *:::::::::*   *:::|
      |*:::::::::::* *::::|
      |::::::::::::: :::::|
    --*-------------*-----+--

And you want the area under the curve . . . got it?