What is area y=28-x^2,y=3x,y= 3/5 x ?

The answer to area y=28-x^2,y=3x,y= 3/5 x is 8958/125

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

area y=28-x^2,y=3x,y= 3/5 x

area

y = 28 - x^{2}, y = 3 x, y = \frac{3}{5} x

\frac{8958}{125}

Decimal

71.664

Solution steps

To find the intersection points solve

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

28 - x^{2} = 3 x : x = - 7, x = 4

28 - x^{2} = \frac{3}{5} x : x = - \frac{28}{5}, x = 5

3 x = \frac{3}{5} x : x = 0

= \int_{- 7}^{- \frac{28}{5}} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{- \frac{28}{5}}^{0} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{0}^{4} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{4}^{5} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 7}^{- \frac{28}{5}} 28 - x^{2} - 3 x d x + \int_{- \frac{28}{5}}^{0} 3 x - \frac{3}{5} x d x + \int_{0}^{4} 3 x - \frac{3}{5} x d x + \int_{4}^{5} 28 - x^{2} - \frac{3}{5} x d x

\int_{- 7}^{- \frac{28}{5}} 28 - x^{2} - 3 x d x = \frac{7399}{750}

\int_{- \frac{28}{5}}^{0} 3 x - \frac{3}{5} x d x = \frac{4704}{125}

\int_{0}^{4} 3 x - \frac{3}{5} x d x = \frac{96}{5}

\int_{4}^{5} 28 - x^{2} - \frac{3}{5} x d x = \frac{149}{30}

= \frac{7399}{750} + \frac{4704}{125} + \frac{96}{5} + \frac{149}{30}

Simplify

= \frac{8958}{125}

What is area y=28-x^2,y=3x,y= 3/5 x ?
The answer to area y=28-x^2,y=3x,y= 3/5 x is 8958/125