3. Integration Flashcards
1
Q
Definite integral
A
The area between the graph and the x-axis over an interval
2
Q
What is the integral of e^x
A
e^x +c
3
Q
What is the integral of 1/x?
A
ln(x) +c
4
Q
How else can {g(x) + h(x) dx be written?
A
{g(x) dx + {h(x) dx
5
Q
How else can {kf(x)dx be written?
A
k{f(x)dx
6
Q
What is integration by parts?
A
Essentially product rule in reverse
If y=uv then y’=u’v+uv’
So
{uv’ dx=uv +{u’v dx +c
7
Q
Substitution rule
A
Essentially reverse chain rule
F(g) +c = {f(g(x))g’(x)dx
8
Q
What is the integral of e^ax?
A
1/a x e^ax +c
9
Q
What is the integral of a^x?
A
1/ln(a) x a^x +c
10
Q
Which types of function are integratable?
A
Any continuous functions
