What is area x^2, 1/2 x^2,3x ?

The answer to area x^2, 1/2 x^2,3x is 45/2

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area x^2, 1/2 x^2,3x

area

x^{2}, \frac{1}{2} x^{2}, 3 x

\frac{45}{2}

Decimal Notation

22.5

Solution steps

To find the intersection points solve

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

x^{2} = \frac{1}{2} x^{2} : x = 0

x^{2} = 3 x : x = 3, x = 0

\frac{1}{2} x^{2} = 3 x : x = 6, x = 0

= \int_{0}^{3} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{0}^{6} ∣ f_{2} (x) - f_{3} (x) ∣ d x

= \int_{0}^{3} x^{2} - 3 x d x + \int_{0}^{6} \frac{1}{2} x^{2} - 3 x d x

\int_{0}^{3} x^{2} - 3 x d x = \frac{9}{2}

\int_{0}^{6} \frac{1}{2} x^{2} - 3 x d x = 18

= \frac{9}{2} + 18

Simplify

= \frac{45}{2}

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