Question

Sketch the regions represented by the following integrals and evaluate them using geometric formulas.

4 integral 1: 2x+3dx

6 integral -2: lx-1l dx (absolute value of x-1

Answer 1

do you mean
4* integral dx/(2x+3)

or what?

Answer 2

4∫1 4 on the top and 1 on the bottom of that sign

6∫-2 same deal

Answer 3

Just use the power rule for these.

∫[1,4] 2x+3 dx = x^2+3x = 24

Recall the definition of |n|:
= n if n >= 0
= -n if n < 0

∫[-2,6] |x-1| dx has to be broken up at x=1, so you get
∫[-2,1] -(x-1) dx + ∫[1,6] (x+1) dx = 17

Answer 4

Thank you so much.

What would the sketched regions look like??

Answer 5

You're in calculus and can't sketch linear functions?

If you type in the integrals as I showed them, wolframalpha.com understands the notation. For example

http://www.wolframalpha.com/input/?i=%E2%88%AB%5B-2,6%5D+%7Cx-1%7C+dx