Area Mania #1

Calculus Level 3

Find the enclosed area (green) \color{#20A900}{\text{(green)}} between the curves :

  • y = x 2 ( b l u e ) y = x^2~~~~~~~~\color{#3D99F6}{(blue)}
  • y = 8 − x 2 ( r e d ) y = 8 -x^2 ~~\color{#D61F06}{(red)}

If your answer is of the form A B \dfrac{A}{B} , where A A and B B are coprime positive integers , then enter the value of A + B A+B .


The answer is 67.

Rishu Jaar by Rishu Jaar , 21, India

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1 solution

Hana Wehbi
Nov 15, 2017

Since it is the area between two parabolas, we can find the area by this method

∫ − 2 2 ( 8 − x 2 − x 2 ) d x = ∫ − 2 2 ( 8 − 2 x 2 ) d x = 64 3 ⟹ A = 64 and B = 3 ⟹ 64 + 3 = 67 . \int_{-2}^{2} (8-x^2-x^2) dx = \int_{-2}^{2} (8-2x^2)dx =\frac{64}{3}\implies A=64 \text{ and } B=3\implies 64+3= \boxed{67}.

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