Calculus Need Help Please/Integrals

Question

. 

Use geometry to evaluate  for  . (4 points)

Answer Choices:

	27
	13.5
	12
	10.5

Answer 1

The graph looks like this:

Since this is a trapezoid, we can calculate the area (the area under the curve or integral) as 1/2(b₁ + b₂)h, where b1 and b2 are base 1 and base 2 and are 6 and 3, and where h is the height which is 3. So:

A = 1/2(b₁ + b₂)h

A = 1/2(6 + 3)3

A = 1/2(9)(3)

A = 27/2 = 13.5