What is area x^{1/4},sqrt(2-x),0 ?

The answer to area x^{1/4},sqrt(2-x),0 is 22/15

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area x^{1/4},sqrt(2-x),0

area

x^{\frac{1}{4}}, 2 - x, 0

\frac{22}{15}

Decimal

1.46666 \dots

Solution steps

To find the intersection points solve

f_{i} (x) = f_{j} (x)

x^{\frac{1}{4}} = 2 - x : x = 1

x^{\frac{1}{4}} = 0 : x = 0

2 - x = 0 : x = 2

= \int_{0}^{1} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{1}^{2} ∣ f_{3} (x) - f_{2} (x) ∣ d x

= \int_{0}^{1} x^{\frac{1}{4}} - 0 d x + \int_{1}^{2} 0 - 2 - x d x

\int_{0}^{1} x^{\frac{1}{4}} - 0 d x = \frac{4}{5}

\int_{1}^{2} 0 - 2 - x d x = \frac{2}{3}

= \frac{4}{5} + \frac{2}{3}

Simplify

= \frac{22}{15}

What is area x^{1/4},sqrt(2-x),0 ?
The answer to area x^{1/4},sqrt(2-x),0 is 22/15