1 Integration of e x ∫ e x.dx = e x + k ∫ e ax+b.dx = e ax+b + k 1a1a.

5
1 Integration of e x ∫ e x .dx = e x + k ∫ e ax+b .dx = e ax+b + k 1 a

Transcript of 1 Integration of e x ∫ e x.dx = e x + k ∫ e ax+b.dx = e ax+b + k 1a1a.

Page 1: 1 Integration of e x ∫ e x.dx = e x + k ∫ e ax+b.dx = e ax+b + k 1a1a.

1

Integration of ex

∫ex.dx = ex + k

∫eax+b.dx = eax+b + k1a

Page 2: 1 Integration of e x ∫ e x.dx = e x + k ∫ e ax+b.dx = e ax+b + k 1a1a.

2

Integration of ex

∫eax+b.dx = eax+b + k1a

Proof

(eax+b) = ddx

eax+b x a = aeax+b

∫a eax+b.dx =

eax+b + k

∫eax+b.dx =

eax+b + k

1a

Page 3: 1 Integration of e x ∫ e x.dx = e x + k ∫ e ax+b.dx = e ax+b + k 1a1a.

3

Integration of ex

Example 1

∫e2x.dx = e2x12

∫eax+b.dx = eax+b + k1a

+ k

Page 4: 1 Integration of e x ∫ e x.dx = e x + k ∫ e ax+b.dx = e ax+b + k 1a1a.

4

Integration of ex

Example 2

∫e3x+1.dx =

13

∫eax+b.dx = eax+b + k1a

1

2

[e3x+1]1

2

13= (e7 –

e4) e7 – e4

3

=Exact = 347.35Approx

Page 5: 1 Integration of e x ∫ e x.dx = e x + k ∫ e ax+b.dx = e ax+b + k 1a1a.

5

Integration of ex

Example 3Find 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.

Exact

= 84.19 units3 Approx

y = ex

y2 = e2x

∫V = π y2.dxa

b

∫V = π e2x.dx0

2

= [e2x]0

2π2

= (e4 – e0]

π2

= (e4 – 1] units3

π2


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