Chapter 13: Q. 16 (page 1004)

Explain how the Fundamental Theorem of Calculus is used in evaluating the iterated integral $\int_{c}^{d} \int_{a}^{b} f (x, y) d x d y$ .

Short Answer

Expert verified

The Fundamental Theorem of Calculus is explained using different steps.

Step by step solution

Step 1. Given Information.

The iterated double integral is,

$\int_{c}^{d} \int_{a}^{b} f (x, y) d x d y$ .

Step 2. Explaining the steps.

The steps to follow are:

Find an anti-derivative of $f (x, y)$ with respect to $x$ .
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.
Now the resultant will be the definite integral of a function with a single variable $y$ .
Find the anti-derivative of the function of step 3 with respect to $y$ .
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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Explain how the Fundamental Theorem of Calculus is used in evaluating the iterated integral $\int_{c}^{d} \int_{a}^{b} f (x, y) d x d y$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explaining the steps.

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

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explaining the steps.

One App. One Place for Learning.

Most popular questions from this chapter

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Explain how the Fundamental Theorem of Calculus is used in evaluating the iterated integral $\int_{c}^{d} \int_{a}^{b} f (x, y) d x d y$ .