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Chapter 4: Q. 0 (page 384)

Read the section and make your own summary of the material.

Short Answer

Expert verified

1. Mean Value Theorem

2. Signed and Absolute Area

3. Average value of a function

Step by step solution

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Step 1. Given information is:

We need to prepare a summary

02

Step 2. Summary

1.Themeanvaluetheoremisdefinedtobeforc鈭�[a,b].2.Foranyintegralfunctionfontheinterval[a,b],a)Thesignedareabetweenthegraphoffandx-axisisgivenbythedefiniteintegral鈭�abf(x)dxb)Theabsoluteareabetweenthegraphoffandx-axisisgivenbythedefiniteintegral鈭�abf(x)dx3.Theaveragevalueofafunctionontheinterval[a,b]isdefinedtobe1b-a鈭�abf(x)dx4.Themeanvaluetheoremisdefinedtobeforc鈭�[a,b]suchthatf'(c)=f(b)-f(a)b-a

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Most popular questions from this chapter

Properties of addition: State the associative law for addition, the commutative law for addition, and the distributive law for multiplication over addition of real numbers. (You may have to think back to a previous algebra course.)

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.

鈭�01鈥�x1+x2dx

What is the difference between an antiderivative of a function and the indefinite integral of a function?

Fill in each of the blanks:

(a) 鈭�x6dx=+C.

(b) is an antiderivative of role="math" localid="1648619282178" x6.

(c) The derivative of is x6.

Without using absolute values, how many definite integrals would we need in order to calculate the absolute area between f(x) = sin x and the x-axis on [-蟺2,2蟺]?

Will the absolute area be positive or negative, and why? Will the signed area will be positive or negative, and why?
See all solutions

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