# 260 Lab 6 - Math 260 Week 6 Lab Name Shelley Adkins...

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Math 260 - Week 6 LabName: Shelley AdkinsAntiderivatives and IntegralsAs we have seen, derivatives give information about instantaneous rates along a curve.The integral, gives information about the area under a curve. Antiderivative: The reverse of the derivative.The original function of a derivative. If f(x) is a derivative, F(x) is the antiderivative.Directions:Look at the examples below then answer questions 1 & 2.Let f(x) be a derivative.f(x) = 3x2f(x) = 5x - 62 133xF(x)x211 10 125x6x5F(x)x6x111234f(x)1xx1344 13443333333333xx3x3xx19xx49xx4F(x)x434343x12x12x12x These problems are asking us to find the antiderivative. In the past to find the derivative we subtracted 1 from the exponent. In this case we are given the derivative f(x). To find the antiderivative F(x) we are adding 1 to the exponent. Simply working backwards. By using this formula we can determine F(x).ʃundu= n+1n+1+C2.) Find the antiderivative of f(x) = 3x5+ x – 4. Show all work. u
3.) How is an antiderivative related to a derivative ? How can that relationship help you to check all of your antiderivative and integral answers on this Lab ?
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