Difference between revisions of "009B Sample Final 2, Problem 1"

Revision as of 19:22, 18 February 2017

(a) State both parts of the Fundamental Theorem of Calculus.

(b) Evaluate the integral

\int _{0}^{1}{\frac {d}{dx}}{\bigg (}e^{\tan ^{-1}(x)}{\bigg )}dx

(c) Compute

{\frac {d}{dx}}\int _{1}^{\frac {1}{x}}\sin t~dt

Solution:

(a)

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

@@ Line 1: / Line 1: @@
-::<span class="exam">a) State '''both parts''' of the Fundamental Theorem of Calculus.
+<span class="exam">(a) State '''both parts''' of the Fundamental Theorem of Calculus.
-::<span class="exam">b) Evaluate the integral
+<span class="exam">(b) Evaluate the integral
-::::<math>\int_0^1 \frac{d}{dx} \bigg(e^{\tan^{-1}(x)}\bigg)dx</math>
+::<math>\int_0^1 \frac{d}{dx} \bigg(e^{\tan^{-1}(x)}\bigg)dx</math>
-::<span class="exam">c) Compute
+<span class="exam">(c) Compute
-::::<math>\frac{d}{dx}\int_1^{\frac{1}{x}} \sin t~dt</math>
+::<math>\frac{d}{dx}\int_1^{\frac{1}{x}} \sin t~dt</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"