Sketch the region R and then use calculus to find the area of R. R is the region between the curve $y = x ^ { 3 }$ and the line y = 6x for x $\ge$ 0.
A) 0
B) 9
C) 1.5
D) 2.25

Question

Quizplus · Accepted Answer

The area of the region is given by the integral of the difference between the two functions from x = 0 to x = 2.$$\int_0^2 (6x - x^3) dx = \left[ 3x^2 - \frac{x^4}{4} \right]_0^2 = 12 - 4 = 8$$

Sketch the Region R and Then Use Calculus to Find y=x3y = x ^ { 3 }y=x3

Sketch the Region R and Then Use Calculus to Find $y = x ^ { 3 }$