MATH 181 Final: m181e1s09
Document Summary
1. (a) di erentiate the function: (b) compute the de nite integral: Solution: (a) using the fundamental theorem of calculus part ii and the chain rule, the derivative of f (x) = ! h(x) g(x) f (t) dt is: F (x) = d dx ! h(x) g(x) f (t) dt h(x) f (g(x)) . Applying the formula to the given function f (x) we get: = f (h(x)) dx d d dx g(x) 2 x# d dx $ x% (b) using the fundamental theorem of calculus part i, the value of the integral is: = [17 ln |5| + 3(5)] [17 ln |1| + 3(1)] = 17 ln 5 + 15 0 3. Problem 2 solution: compute the inde nite integrals: x 1 x dx sin(5 x) dx. Solution: the rst integral is computed using the u-substitution method. Then du = dx du = dx and x = 1 u.
