Integration Method Problems

Antidifferentiation

Example 1 :
Question:

Find the antiderivative for the following function.

f(x) = $e^{3x}$

Solution:

u = 4 - x

= dx

∫14-u^ = 2u^() |14

= -2 - (-4)

= 2

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Integration By Substitution

Example 1 :
Question:

Find the antiderivative for the following function.

f(x) = $e^{3x}$

Solution:

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Integration By Parts

Example 2 :
Question:∫10 xexdx
Solution:

u = x

du = dx

dv = exdx

v = ex

∫udv = uv - ∫vdu

= xex - ∫exdx

= xex - ex |10

= 0 - (0 - 1)

= 1

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