Here's the question you clicked on:
patbatE21
Evaluate the integral by interpreting it in terms of areas. Integral ((1/2)x - (1))dx
|dw:1321990987862:dw|
\[1/4 x^2 - x\] 1/4* 3^2 - 3 - (1/4 * 0^2 - 0) = -3/4
This is a triangle, so we want to look at it that way. Andras seems to have it.
two triangles, sorry
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
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