Question

Find the volume of the solid formed by rotating the region enclosed by
y=e^(1x)+4
y=0
x=0
x=0.3
about the x-axis.

I attempted this problem numerous time and kept on getting 5.501779941pi, using the formale integral of pi(r^2) bounded by 0.3 and 0.

Answer 1

is your function
y = e^x + 4
or
y = e^(x+4) ????

I will assume the first

V = π∫(e^x + 4)^2 dx from 0 to .3
= π∫(e^(2x) + 8e^x + 16) dx
= π[(1/2)e^(2x) + 8e^x + 16x] from 0 to .3
= π( (1/2)e^.6 + 8e^.3 + 16(.3) - ((1/2)e^0 + 8e^0 + 0) )
= π(16.5099 - 8.5) = 25.1639

you better check my arithmetic, it has been failing me lately