Question

How do I find the area enclosed by `x=5y-5y^2` and `x=0`?

Answer 1

`"Area" = 5/6`

Explanation:

Here is a graph of the function:
graph{x=5y-5y^2[-2, 2, -1, 2]}

When `x = 0 =>5y-5y^2 = 0`
`" " => 5y(1-y) = 0`
`" " :. y = 0,1`

So the bounded area is given by:

`A = int_0^1 f(y) \ dy`
`\ \ \ = int_0^1 \ 5y-5y^2 \ dy`
`\ \ \ = 5 \ int_0^1 \ y-y^2 \ dy`
`\ \ \ = 5 \ [ \ y^2/2-y^3/3 \ ]_0^1`
`\ \ \ = 5 \ {(1/2-1/3) - (0-0)}`
`\ \ \ = 5 \ {1/6}`
`\ \ \ = 5/6`