Graph the function and then compute the integral using area.

Question

5

∫ 4x dx

2

Answer 1

integral of 4x is 2x^2

2x^2 evaluated from 2 to 5=

2(5)^2 - 2(2)^2 = 50-8 = 42

4x is a line through the origin, with slope 4, fairly steep.

It creates a diagonal line, for the top of the area. the base is 5-2 = 3

Its height is (4)(5)=20 on the right side and 4(2) = 8 on the left side.

The top area is bh/2 for a right triangle. b=3, h=20-8 = 12. 3(12)/2 = 18.

bottom area is a rectangle 3 by 8 = 24. 24+18 = 42 = total area

Answer 2

∫₂⁵ 4x dx

=[2x²]₂⁵

= (2•5²)-(2•2²)

= 50 - 8 = 42 sq. units