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Popular >

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

Solution

area

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

Solution

\frac{343}{96}

+1

Decimal Notation

3.57291 \dots

Solution steps

Isolate

y

for

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

Isolate

y

for

x + y = 3 : y = 3 - x

f_{1} (x) = \frac{x}{2}

f_{2} (x) = - \frac{x}{2}

To find the intersection points solve

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

\frac{x}{2} = - \frac{x}{2} : x = 0

\frac{x}{2} = 3 - x : x = \frac{9}{4}

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

= \int_{0}^{\frac{9}{4}} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{\frac{9}{4}}^{4} ∣ f_{2} (x) - f_{3} (x) ∣ d x

= \int_{0}^{\frac{9}{4}} \frac{x}{2} - (- \frac{x}{2}) d x + \int_{\frac{9}{4}}^{4} - \frac{x}{2} - (3 - x) d x

\int_{0}^{\frac{9}{4}} \frac{x}{2} - (- \frac{x}{2}) d x = \frac{9}{4}

\int_{\frac{9}{4}}^{4} - \frac{x}{2} - (3 - x) d x = \frac{127}{96}

= \frac{9}{4} + \frac{127}{96}

Simplify

= \frac{343}{96}

Popular Examples

integral of (10x)/(81x^4+49)

\int \frac{10 x}{81 x ^{4} + 49} d x

integral of arccos(x)

\int arccos (x) d x

integral of cos^7(5x)\sqrt[5]{sin(5x)}

integral from-2 to 2 of (x^3-1)

\int_{- 2}^{2} (x^{3} - 1) d x

(\partial)/(\partial x)(x^3+x^2y^3-2y^2)

\frac{\partial}{\partial x} (x^{3} + x^{2} y^{3} - 2 y^{2})

Frequently Asked Questions (FAQ)

What is area x=4y^2,x+y=3 ?
The answer to area x=4y^2,x+y=3 is 343/96