Find the area bounded by the curves y = 4 - x2 and y = 2x + 1
The correct answer is C. 10(2/3) sq. units
y = 4 - x\(^2\) and y = 2x + 1
=> 4 - x2 = 2x + 1
=> x2 + 2x - 3 = 0
(x+3)(x-1) = 0
thus x = 1 or x = -3.
Integrating x\(^2\) + 2x - 3
= 3x - x\(^2\) - \(\frac{x^3}{3}\)
from (1, to -3) : 3 (1) - 1\(^2\) - \(\frac{1^3}{3}\) - 3 (-3) - -3\(^2\) - \(\frac{-3^3}{3}\)
= \(\frac{5}{3}\) + 9
will give 32/3 = 10 \(\frac{2}{3}\)
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