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Popular >

area 10,x,(x^2)/(40)

Solution

area

10, x, \frac{x ^{2}}{40}

Solution

\frac{1100}{3}

+1

Decimal Notation

366.66666 \dots

Solution steps

To find the intersection points solve

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

x = \frac{x ^{2}}{40} : x = 40, x = 0

x = 10 : x = 10

\frac{x ^{2}}{40} = 10 : x = 20, x = - 20

= \int_{- 20}^{0} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{0}^{10} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{10}^{20} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{20}^{40} ∣ f_{2} (x) - f_{1} (x) ∣ d x

= \int_{- 20}^{0} \frac{x ^{2}}{40} - 10 d x + \int_{0}^{10} ∣ x - 10 ∣ d x + \int_{10}^{20} ∣ x - 10 ∣ d x + \int_{20}^{40} \frac{x ^{2}}{40} - x d x

\int_{- 20}^{0} \frac{x ^{2}}{40} - 10 d x = \frac{400}{3}

\int_{0}^{10} ∣ x - 10 ∣ d x = 50

\int_{10}^{20} ∣ x - 10 ∣ d x = 50

\int_{20}^{40} \frac{x ^{2}}{40} - x d x = \frac{400}{3}

= \frac{400}{3} + 50 + 50 + \frac{400}{3}

Simplify

= \frac{1100}{3}

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Frequently Asked Questions (FAQ)

What is area 10,x,(x^2)/(40) ?
The answer to area 10,x,(x^2)/(40) is 1100/3