Jambmaths question:
Find the area bounded by the curve $y=4-{{x}^{2}}$and $y=2x+1$
Option A:
$20\tfrac{1}{3}sq.units$
Option B:
$20\tfrac{2}{3}sq.units$
Option C:
$10\tfrac{2}{3}sq.units$
Option D:
$10\tfrac{1}{3}sq.units$
Jamb Maths Solution:
$\begin{align} & \text{To get the ordinate, equate the two equations} \\ & 4-{{x}^{2}}=2x+1 \\ & {{x}^{2}}+2x-3=0 \\ & (x+3)(x-1)=0 \\ & x=-3\text{ and }x=1 \\ & A=\int_{-3}^{1}{ydx}=\int_{-3}^{1}{(4-{{x}^{2}})}dx-\int_{-3}^{1}{(2x+1)}dx \\ & A=\left[ 4x-\frac{{{x}^{3}}}{3} \right]_{-3}^{1}-\left[ {{x}^{2}}+x \right]_{-3}^{1} \\ & A=\left[ \left( 4(1)-\frac{1}{3} \right)-\left( 4(-3)-\frac{{{(-3)}^{3}}}{3} \right) \right]-\left[ (1+1)-(9-3) \right] \\ & A=\left[ \frac{11}{3}+3 \right]+4=\frac{20}{3}+4=\frac{32}{3}=10\frac{2}{3}sq.units \\\end{align}$
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