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

Question

amistre64 · Answer

it all in the 1st quadrant so we can equate this to:

y = 2 sqrt(x)  and y = x

right?

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

if at any point this makes no sense, just ask