Calculate the area of the plane using the following functions and by the corresponding straights?

Question

f(x) = x^3

y=0
x=1
x=2

Answer 1

I assume you want to find the area between y = 0, y = x^3, x = 1, and x = 2.

Since you're trying to find the area under a curve between 2 points on the x axis, just take the integral of the function from x = 1 to x = 2.
integral of x^3 = 1/4 * x^4
f(1) = 1/4 * 1^4 = 1/4
f(2) = 1/4 * 2^4 = 16/4 = 4

f(2) - f(1) = 3 3/4 (solution!)