Find the area bounded by the curves y = 4 - x2 and y = 2x + 1

  • A 20(1/3) sq. units
  • B 20(2/3) sq. units
  • C 10(2/3) sq. units
  • D 10(1/3) sq. units
jamb 2001mathematics

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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