Question

Find the area of the region between the parabola y^2 = 4x and the line 4x - 3y = 4 Find the area of the region between the parabola y^2 = 4x and the line 4x - 3y = 4 @Mathematics

Answer 1

given\[y^2=4x,\]\[4x-3y=4,\]find points of intersection\[y^2=4+3y,\]\[y^2-3y-4=0,\]\[(y-4)(y+1)=0,\]\[y=4,-1.\]integrate\[\int_{-1}^{4}\int_{\frac{1}{2}y^2}^{\frac{3}{4}y+1}dxdy\]can you do that?

Answer 2

To plug in the upper and lower values and subtrtact them yes

Answer 3

you can also use a single integral if you like

Answer 4

How is that done @satellite73

Answer 5

\[\frac{3}{4}\int_{-1}^{4}ydy+\int_{-1}^{4}dy-\frac{1}{2}\int_{-1}^{4}y^2dy\]