## anonymous 5 years ago Evaluate the integral by interpreting it in terms of areas. Integral ((1/2)x - (1))dx

1. anonymous

|dw:1321990987862:dw|

2. slaaibak

$1/4 x^2 - x$ 1/4* 3^2 - 3 - (1/4 * 0^2 - 0) = -3/4

3. anonymous

|dw:1321991278178:dw|

4. TuringTest

This is a triangle, so we want to look at it that way. Andras seems to have it.

5. TuringTest

two triangles, sorry

6. anonymous

The area that you need is the shaded one on my drawing. Above the x line it is + below it is -. So you need to count 2 triangles

7. agreene

Alternatively, you can split the integral and look at one triangle and one rectangle. $\int\limits_{0}^{3} \frac13x-1dx=\int\limits_{0}^{3}\frac{x}3dx-\int\limits_{0}^{3}1dx$ graphing y=1/3x and y=1 then finding the limits, and remembering you need to subtract one: |dw:1321993923933:dw| You should find: y= 1/3 x from 0,3 to be 3/2 and y=3 from 0,3 to be 3 3/2-3 = -3/2