Volume from Its Slices

Roughly draw the figure
with the h-axis.

At h = h,
the cross sectional area is
S(h) = e^h - 1.

It says to find the volume when h = 3.
So the height of the figure is 3.

So the volume of a figure is
∫₀³ (e^h - 1) dh.

Solve the integral.

Definite Integral: How to Solve

The integral of e^h is itself: e^h.

Integral of e^x

The integral of -1 is -h.

Integral of a Polynomial

Put 3 and 0
into e^h - h.

e⁰ = 1

Zero Exponent

-3 - 1 = -4

So
e³ - 4
is the answer.