Explanation Given : ∂ 2 F ∂ x ∂ y = 6 x 2 y , the rectangle R = [ 0 , 1 ] × [ 0 , 4 ] . Calculation : Step 1: Integrate ∂ 2 F ∂ x ∂ y = 6 x 2 y with respect to x, taking zero as the constant of integration . ∂ F ∂ y = 6 y x 3 3 = 2 y x 3 Step 2: Now integrate with respect to y: F ( x , y ) = 2. y 2 2 x 3 = y 2 x 3 Step 3: As we have already proved in question 50 that ∫ c d ∫ a b ∂ 2 F ∂ x ∂ y d x d y = F ( b , d ) − F ( b , c ) − F ( a + d ) + F ( a , c ) where R = [ a , b ] ...

4th Edition

ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.1, Problem 54E

To determine

The function F(x,y) satisfying the equation $\frac{\partial^{2} F}{\partial x \partial y} = 6 x^{2} y$ and the value of $\int \int_{R} 6 x^{2} y d A$ for the rectangle $R = [0, 1] \times [0, 4]$ .

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Chapter 16.1, Problem 53E

Chapter 16.1, Problem 55E

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Chapter 16 Solutions

ACHIEVE STANDALONE ACCESS F/ CALC 4E

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

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Knowledge Booster

The function F(x,y) satisfying the equation ∂ 2 F ∂ x ∂ y = 6 x 2 y and the value of ∫ ∫ R 6 x 2 y d A for the rectangle R = [ 0 , 1 ] × [ 0 , 4 ] .

Solution Summary: The author explains how to determine the function F(x,y) satisfying the equation 2 F, x and y, with zero as the constant of integration.

The function F(x,y) satisfying the equation $\frac{\partial^{2} F}{\partial x \partial y} = 6 x^{2} y$ and the value of $\int \int_{R} 6 x^{2} y d A$ for the rectangle $R = [0, 1] \times [0, 4]$ .

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Chapter 16 Solutions

The function F(x,y) satisfying the equation ∂ 2 F ∂ x ∂ y = 6 x 2 y and the value of ∫ ∫ R 6 x 2 y d A for the rectangle R = [ 0 , 1 ] × [ 0 , 4 ] .

Solution Summary: The author explains how to determine the function F(x,y) satisfying the equation 2 F, x and y, with zero as the constant of integration.

The function F(x,y) satisfying the equation ∂2F∂x∂y=6x2y and the value of ∫∫R6x2ydA for the rectangle R=[0,1]×[0,4].

Want to see the full answer?

Chapter 16 Solutions

The function F(x,y) satisfying the equation $\frac{\partial^{2} F}{\partial x \partial y} = 6 x^{2} y$ and the value of $\int \int_{R} 6 x^{2} y d A$ for the rectangle $R = [0, 1] \times [0, 4]$ .