March 06, 2014
6.2 Antidifferentiation by Substitution
Definite Integral
b
∫ f(x) dx
U - Substitution
Opposite of the chain rule
(Used when one function is inside of another)
Ex 1)
∫ 3t2(cos t3) dt
a
Indefinite Integral
Ex 2)
∫ f(x) dx
∫ (sin 3x) dx
Ex 4) ∫ √cot x csc2x dx
Ex 3) ∫ (28)(7x -2)3 dx
Ex 5) ∫ (x)(cos 2x2) dx
March 06, 2014
Ex 6)
∫
ln6x
dx
x
Ex 7)
Ex 8) ∫ (sec2x) dx
∫
sin (2t+1)
cos2(2t+1)
dt
6.2 Antidifferentiation by Substitution Day 2
Definite Integral
b
∫ f(x) dx
a
Indefinite Integral
1
Ex 1) ∫ r√1 - r dr
2
0
Ex 2) ∫
1
-1
5r dr
(4 + r2)2
∫ f(x) dx
March 06, 2014
Ex 3) ∫
5
2
dx
2x - 3