Antiderivatives
FTC
More FTC
Finding Bounds
Area Between Curves
100
int(5x^4+x^2-2x+3)dx
F(x)=x^5+1/3x^3-x^2+3x+c
100
What is the first step in doing FTC
ex. int_1^5(8x^3)dx
Take the anti-derivative of the function in the integral
100
Using proper notation, what is the final step of solving the general integral int_a^b(f(x))dx
F(a)-F(b)
100
How do you find the x-intercepts of a function?
Set the function equal to 0
100
How do you algebraically find the x value(s) where two functions intersect?
Set them equal to each other
200
Given that f'(x)=3x^2-x and that f(2)=11 , find f(x)
f(x)=x^3-1/2x^2+5
200
Write an integral to represent the area shaded on the curve of f(x)=-x^2+4x
int_0^4(-x^2+4x)dx
200
Write two integrals needed to find the area shaded on f(x)=(x-1)(x-3)(x-7)
|int_1^3((x-1)(x-3)(x-7))dx|
And
int_3^5((x-1)(x-3)(x-7))dx
200
How do you find the critical points of a function?
Set f'(x)=0
200
What do you do with the functions before integrating to find the area between them?
(Be specific!)
Subtract: Top - Bottom
300
int(4/x^2+1/x)dx
F(x)=-4x^-1+ln|x|+c
OR
F(x)=-4/x+ln|x|+c
300
Evaluate int_0^3(x^2-2x+4)dx
12
300
Evaluate int_1^2(4x^3)dx
15
300
Find the x-values of the x-intercepts of f(x)=x^2-7x+12
x=3 and x=4
300
Find the x-values where the curves f(x)=-x^2+8 and g(x)=x^2 intersect
x=-2 and x=2
Go to 400
400
int(30(5x+3)^5)dx
F(x)=(5x+3)^6+c
400
Evaluate int_2^4(x+1)dx
8
400
Evaluate int_2^3(2x^2)dx and express your answer as an "improper fraction"
38/3
400
Find the x-values of the critical points of the function g(x)=x^3-9x^2
x=0 and
x=6
400
Write a single definite integral with a simplified function to represent the area shaded between f(x)=-x^2+8 and g(x)=x^2
int_-2^2(-2x^2+8)dx
Go to 500
500
Given that h'(x)=10e^(10x) and that h(0)=-2 , find h(x)
h(x)=e^(10x)-3
500
Evaluate int_2^8(2/x)dx and express your answer as an exact value
ln(16)
500
Evaluate int_1^3(2/x^3)dx and express your answer as a fraction
8/9
500
Find the x-value of the point of inflection of f(x)=x^3+x^2
x=-1/3
500
Evaluate the area bound between f(x)=-x^2+8 and g(x)=x^2 Express your answer as an "improper fraction"
Area = 64/3