Question

Find the area of the region bounded by the graphs of the equations. y = 5x2 5, x = 0, x = 2, y = 0

Answer 1

To find the area of the region bounded by the parabola y = 5x^2 and the lines x = 0, x = 2, and y = 0, integrate the function from x = 0 to x = 2. This yields 40/3 or about 13.33 square units.

Step-by-step explanation:

The student is asking to find the area of the region bounded by the parabola y = 5x^2, the lines x = 0, x = 2, and y = 0. To find this area, we need to integrate the function y = 5x^2 from x = 0 to x = 2.

Step-by-Step Solution:

1. Set up the integral for the area under the curve y = 5x^2 between x = 0 and x = 2.
2. Compute the definite integral: ∫02 5x^2 dx.
3. This evaluates to (5/3)x^3 |02, which simplifies to (5/3)(2)^3 - (5/3)(0)^3.
4. Calculate the result: (5/3)(8) - 0 = 40/3 or approximately 13.33 square units.

The calculated area represents the region bounded by the given equations.