Difference between revisions of "009B Sample Final 1, Problem 5"

Revision as of 22:09, 1 February 2016

Consider the solid obtained by rotating the area bounded by the following three functions about the $y$ -axis:

x=0

,

y=e^{x}

, and

y=ex

.

a) Sketch the region bounded by the given three functions. Find the intersection point of the two functions:

$y=e^{x}$ and $y=ex$ . (There is only one.)

b) Set up the integral for the volume of the solid.

c) Find the volume of the solid by computing the integral.

Foundations:

Solution:

(a)

(b)

Step 2:

Step 3:

(c)

Step 1:

@@ Line 3: / Line 3: @@
 ::::::<math>x=0</math>, <math>y=e^x</math>, and <math>y=ex</math>.
-::<span class="exam">a) Sketch the region bounded by the given three functions. Find the intersection point of the two functions:
+<span class="exam">a) Sketch the region bounded by the given three functions. Find the intersection point of the two functions:
-:::<math>y=e^x</math> and <math>y=ex</math>. (There is only one.)
-::<span class="exam">b) Set up the integral for the volume of the solid.
+<span class="exam"><math>y=e^x</math> and <math>y=ex</math>. (There is only one.)
-::<span class="exam">c) Find the volume of the solid by computing the integral.
+<span class="exam">b) Set up the integral for the volume of the solid.
+<span class="exam">c) Find the volume of the solid by computing the integral.
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