Answer:
6.5
Explanation:
You want the definite integral of |2x-3| from -1 to 2 using geometric area formulas.
Area
The attached figure shows the integral to be the sum of the areas of two triangles. The left one has a base of 2.5 and a height of 5; the right one has a base of 0.5 and a height of 1. The areas can be found using the triangle area formula:
A = 1/2bh
A = 1/2(2.5)(5) = 6.25 . . . . . area of left triangle
A = 1/2(0.5)(1) = 0.25 . . . . . area of right triangle
Then the integral is ...
