Tutorial ExerciseEvaluate the iterated integral.'22y(8 + 11x2 + 7y2) dx dyStep 1Observe that the given iterated integral can be rewritten as follows.(8 + 11x2 + 7y2)dx dyStep 2Now integrate the integrand inside the bracket with respect to x by taking y as a constant.12ydy22y(8 + 11x² + 7y²)dx dy8 x11x+7y? x+lyStep 3The Fundamental Theorem of Calculus states that if a function is continuous on the closed interval [a, b] andis an antiderivative of f on the interval [a, b], then9.|f(x)dx = F(b) – F(a).Applying this theorem, we have11x3+ 7y2x3' 8y3+ 14y3 - (8y +311y3+ 7y38х +dy16у + 11dy=lyy +dy.

From the given problem: I=∫02∫y2y8+11x2+7y2dxdy=∫028x+11x33+7y2xy2ydy

Answered: Evaluate the iterated integral. r2y (8…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Evaluate the iterated integral. r2y (8 + 11x2 + 7y²) dx dy ly