Question

Calculate the area of the segment of the curve y^2=4x cut off by the line y=x

Answer 1

it all in the 1st quadrant so we can equate this to:

y = 2 sqrt(x) and y = x

right?

Answer 2

or we can view it from the y axis as: (y^2)/4 = x and y = x

Answer 3

we need an interval; so use system of equation techniques to determine the values

Answer 4

(1/4) y^2 - y = 0

y (1/4 y - 1) = 0; y = 0 and y = 4

Answer 5

given this interval we simply calculate the are under one curve and subtract the given area of the other

Answer 6

\[\int_{0}^{4}(\frac{1}{4}y^2)dy-\int_{0}^{4}y\ dy\]

Answer 7

either way you go dx or dy you get 8/3 i believe

Answer 8

if at any point this makes no sense, just ask