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Popular Calculus >

area y^2=4x,4x-3y=4

Solution

area

y^{2} = 4 x, 4 x - 3 y = 4

Solution

\frac{125}{24}

+1

Decimal

5.20833 \dots

Solution steps

Isolate

y

for

y^{2} = 4 x : y = 2 x, y = - 2 x

Isolate

y

for

4 x - 3 y = 4 : y = - \frac{4 - 4 x}{3}

f_{1} (x) = 2 x

f_{2} (x) = - 2 x

To find the intersection points solve

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

2 x = - 2 x : x = 0

2 x = - \frac{4 - 4 x}{3} : x = 4

- 2 x = - \frac{4 - 4 x}{3} : x = \frac{1}{4}

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

= \int_{0}^{\frac{1}{4}} 2 x - (- 2 x) d x + \int_{\frac{1}{4}}^{4} 2 x - (- \frac{4 - 4 x}{3}) d x

\int_{0}^{\frac{1}{4}} 2 x - (- 2 x) d x = \frac{1}{3}

\int_{\frac{1}{4}}^{4} 2 x - (- \frac{4 - 4 x}{3}) d x = \frac{39}{8}

= \frac{1}{3} + \frac{39}{8}

Simplify

= \frac{125}{24}

Graph

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Frequently Asked Questions (FAQ)

What is area y^2=4x,4x-3y=4 ?
The answer to area y^2=4x,4x-3y=4 is 125/24