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Popular Calculus >

area x=y^4,x=y^5

Solution

area

x = y^{4}, x = y^{5}

Solution

\frac{1}{30}

+1

Decimal

0.03333 \dots

Solution steps

Isolate

y

for

x = y^{4} : y = 4 x, y = - 4 x

Isolate

y

for

x = y^{5} : y = 5 x

f_{1} (x) = 4 x

f_{2} (x) = - 4 x

To find the intersection points solve

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

4 x = - 4 x : x = 0

4 x = 5 x : x = 0, x = 1

- 4 x = 5 x : x = 0

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

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

\int_{0}^{1} 4 x - 5 x d x = \frac{1}{30}

= \frac{1}{30}

Graph

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\frac{d}{d x} (6^{6 - x^{2}})

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d er i v a t i v e y = - 2 x + 7

Frequently Asked Questions (FAQ)

What is area x=y^4,x=y^5 ?
The answer to area x=y^4,x=y^5 is 1/30