1. Integration of ex ∫
ex.dx = ex + k ∫
eax+b.dx = eax+b + k 1 a

2. ∫ ∫ ∫ Integration of ex Proof eax+b.dx = eax+b + k 1 a (eax+b) = d dx
eax+b x a
= aeax+b ∫
a eax+b.dx =
eax+b + k ∫
eax+b.dx =
eax+b + k 1 a

3. ∫ ∫ Integration of ex Example 1 eax+b.dx = eax+b + k 1 a e2x.dx = 1 2

4. ∫ ∫ Integration of ex [e3x+1] = (e7 – e4) 3 Example 2
eax+b.dx = eax+b + k 1 a 2 ∫
e3x+1.dx = 1 3
[e3x+1] 1 2 1 1 3
= (e7 – e4)
e7 – e4 3 = =
Exact
Approx

5. ∫ ∫ Integration of ex Example 3
Find the volume of the solid of revolution made when the curve y = ex is rotated about the x-axis from x = 0 to x = 2.
= [e2x] 2 π
y = ex
y2 = e2x
= (e4 – e0] π 2 ∫
V = π y2.dx a b
= (e4 – 1] units3 π 2
Exact ∫
V = π e2x.dx 2
= units3
Approx