Question

I WILL MARK BRAINLIEST!!! 20 Points!
Philip and Laura want to build a pool in their backyard the length and width of the pool can be represented by the equation f (x) = (x +2) (3x -5) what is the area of Philip in Laura's pool you must show your work include your units of measurement

Again the equation is
f(x) = (x + 2) (3x - 5)​

Answer 1

Answer:

The area of Philip and Laura's pool is 48.68 m².

Step-by-step explanation:

First, find the points where the curve f(x) cut the X-axis.

(x +2) (3x -5) =0

=> x = -2 , 5/3

Now, integrate f(x) dx from -2 to 5/3

∫f(x)dx = ₋₂¹'⁶∫(x + 2) (3x - 5)​ dx                     [Note : ¹'⁶  = ^1.6 = ^5/3]

          =  ₋₂¹'⁶∫(3x² + x - 10)dx

          = x³ + x²/2 + 10x ║[from -2 to 5/3]

          = 125/27 + 25/18 +50/3 + 8 - 2 + 20

          =48.68 m²

Therefore, the area of Philip and Laura's pool is 48.68 m².