MTH 162 Midterm: MTH 162 University of Rochester Midterm1review

• School: University of Rochester
• Department: Mathematics
• Course: MTH 162
• Professor: All

Document Summary

Midterm 1 review sheet: the substitution rule. If u = g(x) is a di erentiable function and f is continuous on the range of g, then. Z f (g(x))g (x) dx = z f (u) du. In the case of de nite integrals, if g (x) is continuous on [a, b] and f is continuous on the range of g, then. Z b a f (g(x))g (x) dx = z g(b) g(a) f (u) du. Suppose f is continuous on [ a, a]. If f is even, i. e. , f ( x) = f (x), then r a. If f is odd, i. e. , f ( x) = f (x), then r a. A f (x) dx = 0: areas between curves. The area of the region bounded by f (x), g(x), x = a, and x = b, where f and g are continuous functions and f (x) g(x) on the interval [a, b], is given by.