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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

If f′ is continuous on [1, 3], then 1 3 f ( v ) d v = f ( 3 ) f ( 1 ) .

To determine

whether the given statement is true or false.

Explanation

Given information:

If f is continuous on [a,b], then the function as follows:

13f(v)dv=f(3)f(1) (1)

Explanation for justification of statement:

Show the Net change theorem as follows:

abF(x)dx=F(b)F(a) (2)

Compare Equation (1) and (2).

Substitute 1 for a and 3 for b in Equation (2)

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