Common Integrals
ƒ x dx
What is (1/2) * x^2
f(x) = -3
F(x) = -3x + c
ƒ 3 dx
What is 3x + c
What is the u-value for ƒ (x+1)^2
What is u = x+1
ƒ ex dx
What is ex + c
f(x) = -6x
F(x) = -3x2 + c
ƒ x2 dx
What is x3/3 + c
Definite Integrals find the area/value between the curve and the ......
What is the x-axis
What is the u-value for ƒ (3x^2+4x+1) *(x^3+2x^2+x)^12 dx
What is u = x^3+2x^2+x +C
f(x) = -24x5 - 10x
F(x) = -4x6 - 5x2 + c
ƒ 5x4 + 2 dx
What is x5 +2x + c
What is the process for the Power Rule for Integration?
What is an add one to the exponent and divide by the new exponent?
What is the u-value for ƒ (ln x)/x dx
ƒ x^2+3x+1 dx
What is (1/3)x^3 + (3/2)x^2 + x +C
f(x) = 4x-5
F(x) = -1/x4 + c
ƒ -9x2 + 10x dx
What is -3x3 + 5x2 + c
If we can't integrate via the Power rule, what rule do we need to use?
What is the Substitution Rule?
What is the u-value for ƒ e^sqrt(x) dx
x^(1/2)
u = sqrt(x)
Note: You'd have to also multiply by 1/2 with a 2 outside the integral.