Area bounded

Calculus Level 5

{ x 2 = y x 2 = − y y 2 = 4 x − 3 \large \begin{cases} x^2=y \\ x^2=-y \\ y^2=4x-3 \end{cases}

Find the area bounded by the curves above. Enter − 1.234 -1.234 as your answer if there is no area bounded by the curves.

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The answer is 0.333.

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Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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1 solution

Graph of region bounded by above three curves will be :

Area \ Bounded \ = \ 2\left( \int _{ 0 }^{ 1 }{ { x }^{ 2 }dx } -\int _{ \frac { 3 }{ 4 } }^{ 1 }{ \sqrt { 4x-3 } dx } \right) = 2 ( 1 3 − 1 6 ) = 1 3 = 0.333 = \ 2\left( \frac { 1 }{ 3 } -\frac { 1 }{ 6 } \right) =\frac { 1 }{ 3 } = \boxed{0.333}

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