Explanation Approach: Definite integral; ∫ a b f ( x ) d x = F ( b ) − F ( a ) Calculation: Consider the given integral: ∫ 0 5 6 x 4 x 2 + 2 y 2 d x Solve: ∫ 0 5 6 x 4 x 2 + 2 y 2 d x = 6 2 ∫ 0 5 x 2 x 2 + y 2 d x Let u = 2 x 2 + y 2 Differentiate both sides: d u = 4 x d x The integral becomes: 6 2 ∫ 0 5 x 2 x 2 + y 2 d x = 6 2 ∫ 0 5 ∫ 1 4 u d x = 6 4 2 [ 2 u ] 0 5 Substitute the value of u :

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Chapter 9.CR, Problem 61CR

To determine

To find:

The value for the integral ∫056x4x2+2y2dx.

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Chapter 9.CR, Problem 60CR

Chapter 9.CR, Problem 62CR

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EBK CALCULUS FOR THE LIFE SCIENCES

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