## anonymous 5 years ago Evaluate the integral below by interpreting it in terms of a partial circle area. In other words, draw a picture of the region the integral represents, and find the area using high school geometry. -9 to 9 sqrt(81-x^2)dx

1. anonymous

well it's a hlaf circle with radius = to 9, so just compute (1/2)pi(r^2), and you've got your integral

2. anonymous

thank you

3. anonymous

no problem

4. anonymous

Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area using high school geometry $\int\limits_{0}^{7}\left| 8x-17 \right|dx$ will we use area of a rectangle for this problem

5. anonymous

it looks like you have to use the area of the rectangle pluss the area of a triangle, the graph is going to be a v shaped based on the line 8x-17, from the point where the vales would normally be negative on the line, they inverse to +y to make the v. in this case you have an area that resembles a trapezoid under the function, so a = 7*17 + (1/2)7*(39-17) these are all from pluging in the values 0 and 7.