Question

The region R bounded by the curve 4y=x² and the lines x=4, y=1. Find the volume of the solid formed when R is rotated completely about (a) the x-axis (b) the y-axis (c) the line y=1(d) the line x=4


the answers should be (a) 52pi/5 (b) 18pi (c) 76pi/15 (d)10pi/3

Answer 1

For the first two, you need to remember two formulas:
\[V_x=π\int\limits_{\inf \lim}^{\sup \lim}y^2 dx\]
\[V_y=π\int\limits_{\inf \lim}^{\sup \lim}x^2 dy\]

For the next two, you'll need to bring the curve to set the limits at the axes to apply the formulas by doing a corresponding translation of the curve

Answer 2

ok thanks so can we go through step by step for the first two, i will try as much as i can and correct me if am wrong.

Answer 3

4y=x^2
y=(x^2)/4
y^2=(x^4)/16
is this correct

Answer 4

Yes

Answer 5

so we integrate this and get x^5/80. how do we get the limits of integration?

Answer 6

You get your limits from the question, though it'll be easier if you sketch out the graph

Answer 7

i have got the sketch the point of intersection is what am struggling with