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Popular >

area 5x,x^2-6,0

Solution

area

5 x, x^{2} - 6, 0

Solution

\frac{305}{6}

+1

Decimal Notation

50.83333 \dots

Solution steps

To find the intersection points solve

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

5 x = x^{2} - 6 : x = 6, x = - 1

5 x = 0 : x = 0

x^{2} - 6 = 0 : x = 6, x = - 6

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

= \int_{- 6}^{- 1} x^{2} - 6 - 0 d x + \int_{- 1}^{0} ∣ 5 x - 0 ∣ d x + \int_{0}^{6} ∣ 5 x - 0 ∣ d x + \int_{6}^{6} x^{2} - 6 - 5 x d x

\int_{- 6}^{- 1} x^{2} - 6 - 0 d x = 46 - \frac{17}{3}

\int_{- 1}^{0} ∣ 5 x - 0 ∣ d x = \frac{5}{2}

\int_{0}^{6} ∣ 5 x - 0 ∣ d x = 15

\int_{6}^{6} x^{2} - 6 - 5 x d x = 39 - 46

= 46 - \frac{17}{3} + \frac{5}{2} + 15 + 39 - 46

Simplify

= \frac{305}{6}

Popular Examples

slope of (-1,6),(2,-6)slope

(- 1, 6), (2, - 6)

(\partial)/(\partial x)((2+x)(y-x))

\frac{\partial}{\partial x} ((2 + x) (y - x))

taylor f(x)=cos(x)taylor

f (x) = cos (x)

f (x) = 5 tan (5 x)

integral of x^2-16x+64

\int x^{2} - 16 x + 64 d x

Frequently Asked Questions (FAQ)

What is area 5x,x^2-6,0 ?
The answer to area 5x,x^2-6,0 is 305/6