What is area-4x+x^2+10,9-2x,2x+1 ?

The answer to area-4x+x^2+10,9-2x,2x+1 is 2/3

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area-4x+x^2+10,9-2x,2x+1

area

- 4 x + x^{2} + 10, 9 - 2 x, 2 x + 1

\frac{2}{3}

Decimal

0.66666 \dots

Solution steps

To find the intersection points solve

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

- 4 x + x^{2} + 10 = 9 - 2 x : x = 1

- 4 x + x^{2} + 10 = 2 x + 1 : x = 3

9 - 2 x = 2 x + 1 : x = 2

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

= \int_{1}^{2} - 4 x + x^{2} + 10 - (9 - 2 x) d x + \int_{2}^{3} - 4 x + x^{2} + 10 - (2 x + 1) d x

\int_{1}^{2} - 4 x + x^{2} + 10 - (9 - 2 x) d x = \frac{1}{3}

\int_{2}^{3} - 4 x + x^{2} + 10 - (2 x + 1) d x = \frac{1}{3}

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

Simplify

= \frac{2}{3}

What is area-4x+x^2+10,9-2x,2x+1 ?
The answer to area-4x+x^2+10,9-2x,2x+1 is 2/3