Miss Battaglia
AP Calculus
Let u be a differentiable function of x.
1.
ò
1
dx = ln x + C
x
2.
ò
1
du = ln u + C
u
Find
ò
x
dx
3
5- x
2
Find the area of the region bounded by the graph of
5
y=
3x +1
the x-axis, and the line x=0 and x=4
Find
ò
x 3 - 3x 2 + 5
dx
x -3
Find
ò
x(x - 2)
dx
3
(x -1)
1.
2.
3.
4.
Learn a basic list of integration formulas
Find an integration formula that resembles all or
part of the integrand, and, by trial and error, find
a choice of u that will make the integrand
conform to the formula.
If you cannot find a u-substitution that works, try
altering the integrand. You might try a trig
identity, multiplication and division by the same
quantity, addition and subtraction of the same
quantity, or long division. Be creative.
If you have access to computer software that will
find antiderivatives symbolically, use it.
ò sin u du = -cosu + C
ò tan u du = -ln cosu + C
ò secu du = ln secu + tan u + C
ò cosu du = sin u + C
ò cot u du = ln sin u + C
ò cscu du = -ln cscu + cot u + C
é pù
Find the average value of f(x) = tanx on the interval 0,
êë
úû
4
Read
5.2 Page 340
#32, 33, 37, 39, 47,
53-59 odd, 67-70,
81, 105-108 all