Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the region of the integral represents, and find the area using basic geometry.

9 integral 0 f(x)=|5x−10| dx

On the calculator i found the answer to be 307...But i feel like i might have done something wrong. help?

Question

Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the region of the integral represents, and find the area using basic geometry.
 
9 integral 0	f(x)=|5x−10| dx

On the calculator i found the answer to be 307...But i feel like i might have done something wrong. help?

agent0smith · Answer

$$\Large \int\limits_{0}^{9} \left| 5x-10 \right|dx$$

Start by drawing a graph of |5x-10| (I assume you're able to do this, if you're in calculus).

agent0smith · Answer

should look like this https://www.google.com/search?q=abs(5x-10)&oq=abs(5x-10)&aqs=chrome..69i57j0.4387j0j7&sourceid=chrome&espv=210&es_sm=93&ie=UTF-8

anonymous · Answer

exactly. then I noticed there are 2 triangles formed underneath the curve, i added their areas together and got 307.

agent0smith · Answer

Doesn't look right... don't forget area of a triangle is half base * height

anonymous · Answer

I recalculated, think I got x and y mixed up. this time I had 1/2(10)(2)+1/2(2-9)(35) = 132.5

agent0smith · Answer

http://www.wolframalpha.com/input/?i=%5Cint%5Climits_%7B0%7D%5E%7B9%7D+%5Cleft%7C+5x-10+%5Cright%7Cdx

agent0smith · Answer

Good job :)