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Theory and ExamplesBy using a substitution, prove that for
Chapter 5, Problem 116E(choose chapter or problem)
Problem 116E
Theory and Examples
By using a substitution, prove that for all positive numbers x and y,
The Shift Property for Definite Integrals A basic property of definite integrals is their invariance under translation, as expressed by the equation.
The equation holds whenever ƒ is integrable and defined for the necessary values of x. For example in the accompanying figure, show that
because the areas of the shaded regions are congruent.
Questions & Answers
QUESTION:
Problem 116E
Theory and Examples
By using a substitution, prove that for all positive numbers x and y,
The Shift Property for Definite Integrals A basic property of definite integrals is their invariance under translation, as expressed by the equation.
The equation holds whenever ƒ is integrable and defined for the necessary values of x. For example in the accompanying figure, show that
because the areas of the shaded regions are congruent.
ANSWER:
Solution:
Step 1 of 3:
In this question, we have to prove that