009B Sample Final 1, Problem 4

This problem has three parts:

a) State the fundamental theorem of calculus.

b) Compute Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\frac {d}{dx}}\int _{0}^{\cos(x)}\sin(t)~dt}

c) Evaluate Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \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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