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

∫ ∫ ∫ 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

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

∫ ∫ 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 = = 347.35 Exact Approx

∫ ∫ 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 = 84.19 units3 Approx