Concept explainers
Substitution: shift 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.
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