Question

Hello I need help with this question thank you

Answer 1

13/2

Explanation:

check the attached file

Answer 2

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 ...

`\displaystyle \int_(-1)^2\,dx=6.25+0.25=\boxed{6.50}`