What is area x^2-11,10x,[-sqrt(11),0]y=0 ?

The answer to area x^2-11,10x,[-sqrt(11),0]y=0 is 830/3

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area x^2-11,10x,[-sqrt(11),0]y=0

area

x^{2} - 11, 10 x, [- 11, 0] y = 0

\frac{830}{3}

Decimal

276.66666 \dots

Solution steps

Isolate

y

for

[- 11, 0] y = 0 : y = 0

f_{1} (x) = 0

f_{2} (x) = x^{2} - 11

To find the intersection points solve

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

0 = x^{2} - 11 : x = 11, x = - 11

0 = 10 x : x = 0

x^{2} - 11 = 10 x : x = 11, x = - 1

= \int_{- 11}^{- 1} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{- 1}^{0} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{0}^{11} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{11}^{11} ∣ f_{3} (x) - f_{2} (x) ∣ d x

= \int_{- 11}^{- 1} 0 - (x^{2} - 11) d x + \int_{- 1}^{0} ∣ 0 - 10 x ∣ d x + \int_{0}^{11} ∣ 0 - 10 x ∣ d x + \int_{11}^{11} 10 x - (x^{2} - 11) d x

\int_{- 11}^{- 1} 0 - (x^{2} - 11) d x = - \frac{11 11 - 1}{3} - 11 + 1111

\int_{- 1}^{0} ∣ 0 - 10 x ∣ d x = 5

\int_{0}^{11} ∣ 0 - 10 x ∣ d x = 55

\int_{11}^{11} 10 x - (x^{2} - 11) d x = - \frac{1331 - 11 11}{3} + 671 - 1111

= - \frac{11 11 - 1}{3} - 11 + 1111 + 5 + 55 - \frac{1331 - 11 11}{3} + 671 - 1111

Simplify

= \frac{830}{3}

What is area x^2-11,10x,[-sqrt(11),0]y=0 ?
The answer to area x^2-11,10x,[-sqrt(11),0]y=0 is 830/3