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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
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 [0, 1], then

0 1 0 1 f ( x ) f ( y ) d y d x = [ 0 1 f ( x ) d x ] 2

To determine

Whether the statement, “ 0101f(x)f(y)dydx=[01f(x)dx]2 ” is true or false.

Explanation

Formula used:

If g(x) is the function of x and h(y) is the function of y then,

abcdg(x)h(y)dydx=abg(x)dxcdh(y)dy (1)

Change of variables doesn’t affect the value of the integral, that is abf(x)dx=abf(y)dy

Reason:

By the equation (1), separate the given integrals

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Chapter 15 Solutions

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