Exam 4 Flashcards
Definite/ Indefinite Integration, U Substitution, Integration by Parts
∫nx to the a
[nx to the (a+1)]/[a+1] + C
∫e to ax
1/a e to the ax + C
∫adx
ax + C
∫ (a/x)
a ln of the absolute value of x
How do you do an initial value problem?
- Find the integral
- Plug in the given coordinates and solve for C
- Write out the whole problem
Two things to do in U Substitution
- Find u, which is the most complicated part of the problem
- Find du, which is the derivative of u
Do not forget…
To add + C at the end of the solved integral
How do you solve definite integrals?
- Solve for the integral
- Plug the top value into the integral minus the bottom value plugged into the integral
In definite integrals, do you need to add C?
No
How do you solve a subdivision problem when given an integral that has numbers not in the given set of rules?
a∫b g(x) dx = a∫n g(x)dx - b∫n g(x)dx
n = same base number
If a∫b f(x)dx = 4, then…
b∫a f(x)dx = -4
a∫a f(x)dx =
0
Net Change of Quantity formula
Q(b) - Q(a) = b∫a Q’(x)dx
What should u, du, dv, and v equal
u = part with x in it or ln
du = derivative of u
dv = other part of problem
v = integral of dv
∫ 1/x to the n
- 1/ (n-1) x to the (n-1)
Integration by parts formula
∫udv = uv - ∫vdu
When should you do integration by parts twice?
When whatever is in ∫vdu cannot be integrated
What should u equal in integration by parts?
Which of the 2 factors gets simpler when you factor it will be your u
Trick to know what u should equal
LIATE
Logs, Inverse Trig, Algebra (x to a/polynomials), expotenst (e to the x)
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