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Chapter 13: Q. 16 (page 1004)

Explain how the Fundamental Theorem of Calculus is used in evaluating the iterated integral鈭�cd鈭�abfx,ydxdy.

Short Answer

Expert verified

The Fundamental Theorem of Calculus is explained using different steps.

Step by step solution

01

Step 1. Given Information.

The iterated double integral is,

鈭�cd鈭�abfx,ydxdy.

02

Step 2. Explaining the steps.

The steps to follow are:

  1. Find an anti-derivative of fx,ywith respect to x.
  2. Use the fundamental theorem of calculus to evaluate the inner integral by evaluating the function from step 1 at b and a and evaluating the difference between them.
  3. Now the resultant will be the definite integral of a function with a single variable y.
  4. Find the anti-derivative of the function of step 3 with respect to y.
  5. Evaluating the function of step 4 at d and c and evaluating the difference between them gives the final result of the double integral of the given function.

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