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U-Substitution
Completing the Square
Sum of Two Quotients
L'Hopital's
Miscellaneous
100
Integrate: cos(x)dx
sin(x)+c
100
The first step to solve a completing the square problem.
What is Complete the Square
100
When do you use sum of two quotients?
When the integral cannot be broken into U and DU
100
Why is L'Hopital's rule used?
To find the limits of indeterminate forms
100
What are four of the main methods of integration that we learned?
U-Substitution Completing the Square Sum of two quotients L'Hopital's Rule
200
Find U and DU: ∫√(3x-1)dx
U: 3x-1 DU: 3dx
200
The trig identities typically used in completing the square problems.
What are inverse trig identities.
200
How is sum of two quotients done?
Separate and solve
200
Give two examples of indeterminate forms.
What are 0/0 and ∞/∞
200
Find new upper and lower limits: 1 ∫x³/(2x^4+1)² 0
Upper: 3 Lower: 1
300
∫sin²(3x)cos²(3x)dx
1/9sin³3x+C
300
Solve: ∫2/(x²-8x+17)
2arctan(x-4)+C
300
Separate: ∫x+2/√(4-x²)
∫x/√(4-x²) + ∫2/√(4-x²)
300
Which indeterminate form is this: lim (x²-2x-3)/(x-3) x→3
0/0
300
What is the integral of (1/(cabin))?
A natural log cabin!
400
Find U, DU, X, DX: ∫√((3x-1)dx
U: 3x-1 DU: 3dx X: (u+1)/3 DX: du/3
400
Solve: ∫dx/(x²-4x+7)
(1/√3)arctan(x-2)/√3 +C
400
Solve: ∫x+2/√(4-x²)
-√(4-x²)/2 + 2arcsin(x/2) + C
400
lim (5x²+3x-1)/(4x²+5) x→∞
5/4
400
What method is used to solve this integral? ∫ 1/(x²+4x+13)
What is completing the square
500
Find new upper and lower limits and solve: 1∫5 x/√(2x-1) 5 ∫x/√(2x-1) 1
Upper: 1 Lower: 3 Solved: 16/3
500
Solve: 9/4 ∫ 1/√(3x-x^2) 3/2
π/6
500
Solve: ∫x-2/√(x²+5)
(1/2)ln|x²+5| - (1/√5)arctan(x/√5) + C
500
Solve: lim cos(x)/x x→∞
0
500
What indeterminate form is used: lim (e^2x-1)/x x→0
0/0