en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

area x+3y=34,x+6=y^2

Solution

area

x + 3 y = 34, x + 6 = y^{2}

Solution

\frac{2197}{6}

+1

Decimal Notation

366.16666 \dots

Solution steps

Isolate

y

for

x + 3 y = 34 : y = \frac{34 - x}{3}

Isolate

y

for

x + 6 = y^{2} : y = x + 6, y = - x + 6

f_{1} (x) = \frac{34 - x}{3}

f_{2} (x) = x + 6

To find the intersection points solve

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

\frac{34 - x}{3} = x + 6 : x = 19

\frac{34 - x}{3} = - x + 6 : x = 58

x + 6 = - x + 6 : x = - 6

= \int_{- 6}^{19} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{19}^{58} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 6}^{19} x + 6 - (- x + 6) d x + \int_{19}^{58} \frac{34 - x}{3} - (- x + 6) d x

\int_{- 6}^{19} x + 6 - (- x + 6) d x = \frac{500}{3}

\int_{19}^{58} \frac{34 - x}{3} - (- x + 6) d x = \frac{399}{2}

= \frac{500}{3} + \frac{399}{2}

Simplify

= \frac{2197}{6}

Popular Examples

derivative of 9x^2e^{-x}

\frac{d}{d x} (9 x^{2} e^{- x})

derivative of f(x)=sqrt(5/2+3/2 x)derivative of

f (x) = \frac{5}{2} + \frac{3}{2} x

integral of x^2\sqrt[3]{(x)(x^4)(x^3)}

derivative of (arctan(7x))^2 derivative of

(arctan (7 x))^{2}

sum from n=0 to infinity of 4/(3^{n-1)}

n = 0 \sum \infty \frac{4}{3 ^{n - 1}}

Frequently Asked Questions (FAQ)

What is area x+3y=34,x+6=y^2 ?
The answer to area x+3y=34,x+6=y^2 is 2197/6