Integration By Parts
The purpose of integration by parts is to...
What is to integrate multiple functions that are multiplied together?
The purpose of trig substitution is to do this.
What is to substitute in terms of Dθ and θ?
The two methods that are use to integrate rational functions
What is Partial Fraction Decomposition and Rational Long Division?
The Midpoint Rule is a version of this approximation technique
What is Riemann Sums?
These are the three classifications of improper integrals
What is:
- One of the limits are either ∞ or -∞
- Both of the limits are ∞
- One of the limits are undefined
The order that should be used when doing integration by parts.
What is LIATE (Logarithmic, Inverse Trigonometric, Algebraic, Trigonometric, Exponential)?
The identity for a2+x2 is...
What is 1+tan2(θ)=sec2(θ)?
You have to follow this rule for long division using rational numbers.
What is having the highest power in the numerator or both the numerator and denominator having the same highest power?
This rule is used for approximating with this quadrilateral.
What is the Trapezoidal Rule?
One of the conditions of Case One of improper integration.
What is replace the upper infinite boundary with the variable b?
This is the form that integration by parts is set.
What is ∫ udv=uv-∫ vdu ?
This is used when finding trigonometric identities
What is the Pythagorean Theorem?
This is what indicates that partial fraction decomposition needs to be used.
What is the denominator has the highest power in the function?
Simpson's Rule uses what to approximate the function.
What is a quadratic curve?
This done when applying Case Three of improper integration
What is create two improper integrals from replacing ∞ and -∞ with a variable?
The answer to the problem ∫ 6xe4x dx
What is 6((xe4x/4)-(e4x/16))+C ?
The integral for ∫ sec(ax) dx
What is 1/a ln |sec(ax)+tan(ax)| + C ?
You have to do this in order to write out partial fraction.
What is factoring?
The formula used for the Trapezoidal Rule
Area=1/2 h(b1+b2)
This should be done when you have an undefined upper and lower limit
What is find the limit of the new expression as c approaches the undefined value from the right or left?
The answer to the problem ∫ sin-1(x) dx
What is ∫ (xsin-1(x)+sqrt(1-x2))+C ?
The answer to ∫ 1/sqrt(x2+36) dx
What is ln|((sqrt(x2+36))+x)/6|+C ?
The answer to ∫ (3x+9)/(x2-4x-5) dx
What is 4ln|x-5| - ln|x-1|+C ?
Simpson's Rule follows this order
What is (f(x0) + 4f(x1) + 2f(x2) + 4f(x3) +...+ f(xn))?
The answer to ∫08 (1/sqrt3(8-x)) dx
What is 6 and the integral converges.