Term
What is the Antiderivative of this?
Ax^ndx
If n is not equal to -1
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Definition
A(1/n+1)x^(n+1)+C
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Term
What is the Antiderivative of this?
Ax^ndx
If n is equal to -1
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Definition
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Term
What is the Antiderivative of this?
e^kxdx
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Definition
(1/k)e^kx+C
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Term
What are tips for finding the antiderivative in which there is a 'u'?
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Definition
1.) Find u'
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2.) Set the original function next to 1/u' and factor out common factors between the A value of the original function and u'.
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3.) Multiply them together
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4.) Take the antiderivative of the function unless the function is exponential in which for some reason you just add "+C", substitute the value of 'u' back in, and your done.
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Term
How do you take the definitive integral of a function, when trying to find the area within the integral of a to b?
[a is always the smaller number]
[the integral is always defined on the x-axis]
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Definition
1.) Find the antiderivative of f(x)
[Don't add the +C at the end]
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2.) Your function is now:
f(x) = the antiderivative of f(x)
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3.) Find f(a)
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4.) Find f(b)
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5.) f(b)-f(a)
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Term
If you have two triangles, and one triangle is inside of the other, how do you find the area of just one of the triangles?
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Definition
Find the area of both triangles, then subtract the area of the triangle that is inside of the other triangle, from the other triangle.
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Term
If you have to find the total area, and are presented with two integrals, what do you do?
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Definition
Find the definite integral of both, take the absolute value of both definite integrals, and add them together.
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Term
If an integral crosses the x-axis, to find the area, you will need to...?
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Definition
Take two definite integrals
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