6.1 & 6.4 an overview of the area problem area
Post on 30-Jul-2015
392 Views
Preview:
TRANSCRIPT
Integration by Substitution
Recognizing the “Outside-Inside” Pattern
From doing derivatives we need to recognize the integrand above is a composite function from the from the ““derivative of the outside times derivative of the outside times the derivative of the insidethe derivative of the inside”” (chain rule). (chain rule).
Cx 32 1
3
1 “+ C” since this is an indefinite integral
Think of this function as 2 functions: f(x) and g(x)
As a composite function then:
Now look at the original integral:
2xxf 12 xxg
22 1 xxgf
insideoutside
f(g(x)) g’(x)
Read this as “the antiderivative of the outside function with the inside function plugged in…plus C”
Let’s Practice !!!
Let u = x3
du = 3x2
du sin u
Let u = x4 + 2
du = 4 x3
1/4 4
u du
More Practice !!!
Here are some problems for you to work on!!!
Less Apparent Substitution
Let u = x – 1 du = dx
x = u + 1x2 = (u + !)2
(u + 1) u du
top related