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

Revision as of 20:02, 1 February 2016

We would like to evaluate

{\frac {d}{dx}}{\bigg (}\int _{-1}^{x}\sin(t^{2})2tdt{\bigg )}

.

a) Compute

f(x)=\int _{-1}^{x}\sin(t^{2})2tdt

.

b) Find

f'(x)

.

c) State the fundamental theorem of calculus.

d) Use the fundamental theorem of calculus to compute

{\frac {d}{dx}}{\bigg (}\int _{-1}^{x}\sin(t^{2})2tdt{\bigg )}

without first computing the integral.

Foundations:

Solution:

(a)

(b)

Step 2:

Step 3:

(c)

Step 1:

@@ Line 1: / Line 1: @@
+<span class="exam"> We would like to evaluate
+:::::<math>\frac{d}{dx}\bigg(\int_{-1}^{x} \sin(t^2)2tdt\bigg)</math>.
+::<span class="exam">a) Compute <math>f(x)=\int_{-1}^{x} \sin(t^2)2tdt</math>.
+::<span class="exam">b) Find <math>f'(x)</math>.
+::<span class="exam">c) State the fundamental theorem of calculus.
+::<span class="exam">d) Use the fundamental theorem of calculus to compute <math>\frac{d}{dx}\bigg(\int_{-1}^{x} \sin(t^2)2tdt\bigg)</math> without first computing the integral.
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Foundations: &nbsp;