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If $ a $ and $ b $ are positive numbers, show tha…
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Problem 90 Hard Difficulty

If $ f $ is continuous on $ \mathbb{R} $, prove that
$$ \int^b_a f(x + c) \, dx = \int^{b + c}_{a + c} f(x) \, dx $$
For the case where $ f(x) \ge 0 $, draw a diagram to interpret this equation geometrically as an equality of areas.

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Calculus 1 / AB
Calculus: Early Transcendentals

Chapter 5

Integrals

Section 5

The Substitution Rule

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Video Transcript

we know that for this question, withdrawing the diagram The first thing you could do a substitute you is expose. See, this indicates that D axe is do you? Because it's just one as the derivative of X. Therefore, in of the limits of integration, change to a pussy on the bottom and people see on the top after vax d axe Remember wise half of Expo See you had shifted by C units in the left direction horizontally after vax on the right and affects was seeing left.

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