Difference between revisions of "009B Sample Final 2, Problem 5"

Revision as of 20:19, 17 February 2017

a) Find the area of the surface obtained by rotating the arc of the curve

y^{3}=x

between

(0,0)

and

(1,1)

about the

y

-axis.

b) Find the length of the arc

y=1+9x^{\frac {3}{2}}

between the points

(1,10)

and

(4,73).

Solution:

(a)

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

@@ Line 1: / Line 1: @@
-<span class="exam">Consider the region bounded by the following two functions:
+::<span class="exam">a) Find the area of the surface obtained by rotating the arc of the curve
-::::::::<span class="exam"> <math style="vertical-align: -5px">y=2(-x^2+9)</math> and <math style="vertical-align: -4px">y=0</math>.
-<span class="exam">a) Using the lower sum with three rectangles having equal width, approximate the area.
+::::<math>y^3=x</math>
-<span class="exam">b) Using the upper sum with three rectangles having equal width, approximate the area.
+::<span class="exam">between <math>(0,0)</math> and <math>(1,1)</math> about the <math>y</math>-axis.
-<span class="exam">c) Find the actual area of the region.
+::<span class="exam">b) Find the length of the arc
+::::<math>y=1+9x^{\frac{3}{2}}</math>
+::<span class="exam">between the points <math>(1,10)</math> and <math>(4,73).</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"