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

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

View answer & explanation

Correct answer is C

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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