Question

FIND THE VOLUME OF THE SOLID OBTAINED BY ROTATING THE REGION BOUNDED BY THE GIVEN CURVES ABOUT THE SPECIFIED AXIS.

y=e^x, y=0, x=0, x=1, ABOUT THE x-axis

Answer 1

we know that volume of the solid obtained by rotating the region bounded by y = f(x) and y = 0 between x = a and x = b about x axis is given by,

Tf(x))da V

we have a = 0, b = 1 and f(x) = e^x hence volume is given by,

T(e)2d V

2r те V

2da V = T

e2r V = T 2 1

V = e2(1) -e2(0)

V [e2- 1