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

Revision as of 18:46, 19 January 2016

Consider the region $S$ bounded by $x=1,x=5,y={\frac {1}{x^{2}}}$ and the $x$ -axis.

a) Use four rectangles and a Riemann sum to approximate the area of the region

S

. Sketch the region

S

and the rectangles and indicate your rectangles overestimate or underestimate the area of

S

.

b) Find an expression for the area of the region

S

as a limit. Do not evaluate the limit.

Solution:

Final Answer:

@@ Line 1: / Line 1: @@
-<span class="exam">Evaluate the indefinite and definite integrals.
+<span class="exam">Consider the region <math>S</math> bounded by <math>x=1,x=5,y=\frac{1}{x^2}</math> and the <math>x</math>-axis.
-::<span class="exam">a) <math>\int x^2\sqrt{1+x^3}dx</math>
+::<span class="exam">a) Use four rectangles and a Riemann sum to approximate the area of the region <math>S</math>. Sketch the region <math>S</math> and the rectangles and indicate your rectangles overestimate or underestimate the area of <math>S</math>.
-::<span class="exam">b) <math>\int _{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{\cos(x)}{\sin^2(x)}dx</math>
+::<span class="exam">b) Find an expression for the area of the region <math>S</math> as a limit. Do not evaluate the limit.