en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

area y=3x,x=8-y^2

Solution

area

y = 3 x, x = 8 - y^{2}

Solution

\frac{4913}{162}

+1

Decimal Notation

30.32716 \dots

Solution steps

Isolate

y

for

x = 8 - y^{2} : y = - x + 8, y = - - x + 8

f_{1} (x) = 3 x

f_{2} (x) = - x + 8

To find the intersection points solve

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

3 x = - x + 8 : x = \frac{8}{9}

3 x = - - x + 8 : x = - 1

- x + 8 = - - x + 8 : x = 8

= \int_{- 1}^{\frac{8}{9}} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{\frac{8}{9}}^{8} ∣ f_{3} (x) - f_{2} (x) ∣ d x

= \int_{- 1}^{\frac{8}{9}} 3 x - (- - x + 8) d x + \int_{\frac{8}{9}}^{8} - - x + 8 - - x + 8 d x

\int_{- 1}^{\frac{8}{9}} 3 x - (- - x + 8) d x = \frac{817}{162}

\int_{\frac{8}{9}}^{8} - - x + 8 - - x + 8 d x = \frac{2048}{81}

= \frac{817}{162} + \frac{2048}{81}

Simplify

= \frac{4913}{162}

Popular Examples

derivative of 15

\frac{d}{d x} (15)

integral of (2cos(x)-3sin(x)+x)

\int (2 cos (x) - 3 sin (x) + x) d x

derivative of f(x)=(6x+7)(7x-8)derivative of

f (x) = (6 x + 7) (7 x - 8)

integral of 10sin(5x)

\int 10 sin (5 x) d x

integral of (1+2x^2)^2

\int (1 + 2 x^{2})^{2} d x

Frequently Asked Questions (FAQ)

What is area y=3x,x=8-y^2 ?
The answer to area y=3x,x=8-y^2 is 4913/162