Question

Find the area of the region bounded by the parabola x=y^2 +2 and the line y=x-8

Answer 1

The area of the region bounded by the parabola x = y² + 2 and the line y = x - 8 is; -125/6

How to find the integral boundary area?

We want to find the area of the region bounded by the parabola x = y² + 2 and the line y = x - 8.

Let us first try to found the two boundary points.

Put y² + 2 for x in the line equation to get;

y = y² + 2 - 8

y² - y - 6 = 0

From quadratic root calculator, we know that the roots are;

y = -2 and 3

Thus, the area will be the integral;

Area = ∫³₋₂ (y² - y - 6)

Integrating gives;

¹/₃y³ - ¹/₂y - 6y|³₋₂

Plugging in the integral boundary values and solving gives;

Area = -125/6

Read more about Integral Boundary Area at; brainly.com/question/23277151

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