Term
How do you find an antiderivative?
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Definition
1.)If it is in this format: x^ndx
Use the Power Rule of Antiderivatives
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2.) If it is in this format:
Ax^bdx=?
You will do the following:
A(1/b)x^(b+1)+C
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3.) If it is in this format:
(Ax^2 - Bx + C)dx = ?
You will do the following:
Ax^2dx - Bxdx + Cdx
and use this edited Power Rule of Antiderivatives on Each Individual Part
x^ndx = (1/n+1)x^(n+1)
Where n cannot equal -1
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4.) If it is 1dx your solution is:
x+C
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5.) If x^-ndx:
ln|x| + C or 1/x+C
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Term
What is the antiderivative of 2x?
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Definition
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Term
Why is there a C, in the antiderivative of 2x?
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Definition
Because you have to account for the possible existence of a constant.
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Term
What is the notation for writing the integral of 2x?
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Definition
2xdx = x^2+C
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Term
What is the Power Rule of Antiderivatives?
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Definition
x^ndx = (1/n+1)x^(n+1)+C
Where n cannot equal -1
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Term
What does 1dx=?
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Definition
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Term
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Definition
x^bdx=A
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A(1/b)x^(b+1)+C
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Term
(Ax^2 - Bx + C)dx = ?
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Definition
Ax^2dx - Bxdx + Cdx
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Term
What is the Antiderivative Rule of Exponential Functions?
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Definition
1.) if:
e^xdx = e^x + C
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2.) If:
Ae^xdx = (1/Ae^(Ax))+C
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Term
What does A/(B/C)=?
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Definition
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Term
If you have a function with three variables and you know the values of two of the variables, how do you determine the value of the third variable?
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Definition
Plug in the two values you know, and solve for the unknown variable.
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