Question

Write a definite integral that represents the area of the region. (Do not evaluate the integral.) y1 = x2 − 5x y2 = 0

Answer 1

Answer: Area =
`\int\limits^5_0 {(5x - x^2)} \, dx`

Explanation:

Thiis is quite straightforward, so I will be gudiding you through the process.

we have that;

y1 = x² -5x

and y² = 0

Taking Limits:

y1 = x² -5x, y2 = 0

x² - 5x = 0;

so x(x - 5) = 0

this gives x = 0 and x = 5

∴ 0≤x≤5

This is to say that the graph intersets at x = 0 and x = 5 and y2 is the upper most function.

Let us take the formula:

Area = ∫b-a (upper curve - lower curve)

where a here represents 0 and b represents 5

the upper curve y2 = 0

whereas the lower curve y1 = x² - 5x

Area = ∫5-0 [ 0 - (x² - 5x) ] dx

This becomes the Area.

Area =
`\int\limits^5_0 {(5x - x^2)} \, dx`

cheers i hope this helped !!!