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Popular >

area x,7,(x^2)/(28)

Solution

area

x, 7, \frac{x ^{2}}{28}

Solution

\frac{539}{3}

+1

Decimal Notation

179.66666 \dots

Solution steps

To find the intersection points solve

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

x = \frac{x ^{2}}{28} : x = 28, x = 0

x = 7 : x = 7

\frac{x ^{2}}{28} = 7 : x = 14, x = - 14

= \int_{- 14}^{0} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{0}^{7} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{7}^{14} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{14}^{28} ∣ f_{2} (x) - f_{1} (x) ∣ d x

= \int_{- 14}^{0} \frac{x ^{2}}{28} - 7 d x + \int_{0}^{7} ∣ x - 7 ∣ d x + \int_{7}^{14} ∣ x - 7 ∣ d x + \int_{14}^{28} \frac{x ^{2}}{28} - x d x

\int_{- 14}^{0} \frac{x ^{2}}{28} - 7 d x = \frac{196}{3}

\int_{0}^{7} ∣ x - 7 ∣ d x = \frac{49}{2}

\int_{7}^{14} ∣ x - 7 ∣ d x = \frac{49}{2}

\int_{14}^{28} \frac{x ^{2}}{28} - x d x = \frac{196}{3}

= \frac{196}{3} + \frac{49}{2} + \frac{49}{2} + \frac{196}{3}

Simplify

= \frac{539}{3}

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Frequently Asked Questions (FAQ)

What is area x,7,(x^2)/(28) ?
The answer to area x,7,(x^2)/(28) is 539/3