Perhaps the simplest change of variables is the shift or translation given by u = x + c, where c is a real number.

a. Prove that shifting a function does not change the net area under the curve, in the sense that

b. Draw a picture to illustrate this change of variables in the case that f(x) = sin x, a = 0, b = π, and c = π/2.

Transcribed Image Text:

Го •b+c f(u) du. f(x + c) dx = a+c