We take u = 4 – x du = (-1)dx Let's label the limits of integration as x-values so we don't mess up. We're not done with the substitution yet. We still have to change the limits of integration so we have u-values instead of x-values. When x = 2, u = 4 – (2) = 2. When x = -1, u = 4 – (-1) = 5. Here's what the integral looks like after the limits of integration are changed: Now that we've changed the limits of integration, we're done with the substitution. From here, we can use the FTC to integrate. We conclude that Be Careful: When using substitution to evaluate a definite integral, we aren't done with the substitution part until we've changed the limits of integration. |