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Popular >

area x,1,(x^2)/4

Solution

area

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

Solution

\frac{11}{3}

+1

Decimal

3.66666 \dots

Solution steps

To find the intersection points solve

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

x = \frac{x ^{2}}{4} : x = 4, x = 0

x = 1 : x = 1

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

= \int_{- 2}^{0} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{0}^{1} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{1}^{2} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{2}^{4} ∣ f_{2} (x) - f_{1} (x) ∣ d x

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

\int_{- 2}^{0} \frac{x ^{2}}{4} - 1 d x = \frac{4}{3}

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

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

\int_{2}^{4} \frac{x ^{2}}{4} - x d x = \frac{4}{3}

= \frac{4}{3} + \frac{1}{2} + \frac{1}{2} + \frac{4}{3}

Simplify

= \frac{11}{3}

Graph

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y = 600 - \frac{x ^{2}}{121}

x^{^{'}} = x - x^{2}

derivative of e^{2x}+e^{-2x}

\frac{d}{d x} (e^{2 x} + e^{- 2 x})

integral of e^{iwt+ibt}

\int e^{i wt + ib t} d t

Frequently Asked Questions (FAQ)

What is area x,1,(x^2)/4 ?
The answer to area x,1,(x^2)/4 is 11/3