What is area y=2x^2,y=8x^2,3x+y=5 ?

The answer to area y=2x^2,y=8x^2,3x+y=5 is 1097/128

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

area y=2x^2,y=8x^2,3x+y=5

area

y = 2 x^{2}, y = 8 x^{2}, 3 x + y = 5

\frac{1097}{128}

Decimal

8.5703125

Solution steps

Isolate

y

for

3 x + y = 5 : y = 5 - 3 x

f_{1} (x) = 2 x^{2}

f_{2} (x) = 8 x^{2}

To find the intersection points solve

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

2 x^{2} = 8 x^{2} : x = 0

2 x^{2} = 5 - 3 x : x = 1, x = - \frac{5}{2}

8 x^{2} = 5 - 3 x : x = \frac{5}{8}, x = - 1

= \int_{- \frac{5}{2}}^{- 1} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{- 1}^{0} ∣ f_{2} (x) - f_{1} (x) ∣ d x + \int_{0}^{\frac{5}{8}} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{\frac{5}{8}}^{1} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- \frac{5}{2}}^{- 1} 2 x^{2} - (5 - 3 x) d x + \int_{- 1}^{0} 8 x^{2} - 2 x^{2} d x + \int_{0}^{\frac{5}{8}} 2 x^{2} - 8 x^{2} d x + \int_{\frac{5}{8}}^{1} 2 x^{2} - (5 - 3 x) d x

\int_{- \frac{5}{2}}^{- 1} 2 x^{2} - (5 - 3 x) d x = \frac{45}{8}

\int_{- 1}^{0} 8 x^{2} - 2 x^{2} d x = 2

\int_{0}^{\frac{5}{8}} 2 x^{2} - 8 x^{2} d x = \frac{125}{256}

\int_{\frac{5}{8}}^{1} 2 x^{2} - (5 - 3 x) d x = \frac{117}{256}

= \frac{45}{8} + 2 + \frac{125}{256} + \frac{117}{256}

Simplify

= \frac{1097}{128}

x \to - 4 lim (2 x + 1)

x y^{^{'}} = (y + 1) (x + 1)

\frac{d}{d x} (arcsin (2))

\int \frac{1}{( 9 + x ^{2} )} d x

\frac{d}{d x} (65 - 25 sin^{2} (x))

What is area y=2x^2,y=8x^2,3x+y=5 ?
The answer to area y=2x^2,y=8x^2,3x+y=5 is 1097/128