💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!



Numerade Educator



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.



More Answers


You must be signed in to discuss.

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.