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

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- Mar 18th 2006, 12:15 PMfrozenflamesArea 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 - Mar 18th 2006, 01:52 PMCaptainBlackQuote:

Originally Posted by**frozenflames**

close to 12 (so answer (D) is probably correct), but we will finish thsi using

integration.

$\displaystyle

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

$

RonL