Volume (1 Viewer)

[Kutay]

hey sorry for all the questions but having a problem

'Calculate the volume of the solid generated when the region in the first quadrant bounded by the curved y = e^x, the line x = IN 2 and the coordinate axis, is rotated about the x-axis

 

[Xayma]

First of all, these would have been better put in one single thread, even as seperate posts.
I'm guessing IN 2=ln 2 ie log_e 2


V=π∫ y² dx

y=e^x
∴
y²=(e^x)²
=e^2x

V=π^{ln 2}₀∫e^2x dx
=π[1/2*e^2x]^{ln 2}₀
=π/2[e^2x]^{ln 2}₀
=π/2[e^2ln2-e⁰]
=π/2[e^ln2²-e⁰]
=π/2[e^ln4-e⁰]
=π/2[4-1]
=3π/2 units³

Meh cant be bothered checking the working too much code in the way so I hope it's right