009B Sample Final 1, Problem 4

This problem has three parts:

a) State the fundamental theorem of calculus.

b) Compute ${\frac {d}{dx}}\int _{0}^{\cos(x)}\sin(t)~dt$

c) Evaluate $\int _{0}^{\frac {\pi }{4}}\sec ^{2}x~dx$

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Step 3:

(c)

Step 1:

Step 2:

Final Answer:
(a)
(b)
(c)

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