need help please!!!!

Question

find the area bounded by the curves y=8x-x^2 and y=3x

Answer 1

Hi Melissa,

First you need to find the points of intersection of the two curves by setting 3x = 8x - x².

This should result in x²-5x = 0 , giving points of intersection where x = 0 or x = 5.

You need a sketch of the graph to get an idea whether or not one of the graphs is always greater than the other. See the following:

https://www.desmos.com/calculator/i8rputebo9

Looks like the length of a typical rectangle can be represented by (8x - x²) - 3x. In the Desmos graph F(x) represents an anti-derivative of that expression.

The definite integral could have been written as: ∫₀⁵ (-x² + 5x) dx which would give a slightly different looking anti derivative. -1/3 x³ +5/2 x² |₀⁵ (same result)