Find the area enclosed by the curve

Calculus Level 3

x 4 5 + y = 1 \large x^{\frac 45} + |y| = 1

The set of points ( x , y ) (x, y) satisfying the equation above form a curve enclosing a region. If the area of this region can be expressed as a b \dfrac ab , where a a and b b are coprime positive integers, find a + b a+b .


The answer is 25.

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