## patbatE21 Group Title Evaluate the integral by interpreting it in terms of areas. Integral ((1/2)x - (1))dx 2 years ago 2 years ago

1. patbatE21 Group Title

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2. slaaibak Group Title

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

3. Andras Group Title

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4. TuringTest Group Title

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

5. TuringTest Group Title

two triangles, sorry

6. Andras Group Title

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 Group Title

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