Question

Which is the area of the region in quadrant I bounded by y = 2x² and y = 2x³?

A) ∫(2x³ - 2x²) dx from 0 to 1
B) ∫(2x² - 2x³) dx from 0 to 1
C) ∫(2x² - 2x³) dx from 0 to 2
D) ∫(2x³ - 2x²) dx from 0 to 2

Answer 1

The area of the region in quadrant I bounded by y = 2x² and y = 2x³ can be found by evaluating the integral ∫(2x³ - 2x²) dx from 0 to 1.

Step-by-step explanation:

To find the area of the region in quadrant I bounded by y = 2x² and y = 2x³, we need to determine the limits of integration and set up the integral. The curves intersect when 2x² = 2x³, which simplifies to x² = x³. Solving for x, we find that x = 0 and x = 1.

The correct integral to find the area is ∫(2x³ - 2x²) dx from 0 to 1, which is option A. Evaluating this integral will give you the area of the region in quadrant I bounded by the curves.