MATH 7 Santa Monica College Calculus Math Question Solve this 3 question really clear and make sure the answer is correct. Also, Please make sure you have all the steps written down thanks. MATH 7 ADDITIONAL PROBLEM
KIM, SUNGJIN
Problem 1. Let a < b. Define a function F by
Z x
(t − a)2 (t − b) dt.
F (x) =
a
(a) Show that b is a critical number of F . (5 pts)
(b) Show that for any n 6= −1,
Z
(t − a)n+1
+ C.
n+1
(t − a)n dt =
(5 pts)
(c) Show that F attains the minimum at x = b, and that
F (b) = −
(5 pts)
1
(b − a)4
.
12
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