# Area Problem

• March 18th 2006, 12:15 PM
frozenflames
Area Problem
12. The area of the region enclosed by the graph of y = x^2 + 1 and the line y = 5 is

(A) 14/3
(B) 16/3
(C) 28/3
(D) 32/3
(E) 8p
• March 18th 2006, 01:52 PM
CaptainBlack
Quote:

Originally Posted by frozenflames
12. The area of the region enclosed by the graph of y = x^2 + 1 and the line y = 5 is

(A) 14/3
(B) 16/3
(C) 28/3
(D) 32/3
(E) 8p

Sketch the graph, see attachment. Counting squares indicates this area is
close to 12 (so answer (D) is probably correct), but we will finish thsi using
integration.

$
\rm{Area} = \int_2^2 5-(x^2+1)\ dx=\int_2^2 4-x^2\ dx$
$=\left[4x-x^3/3\right]_{-2}^2=(8-8/3) - (-8+8/3)=32/3
$

RonL