What is area 2y=5sqrt(x),y=5,2y+4x=9 ?

The answer to area 2y=5sqrt(x),y=5,2y+4x=9 is 235/48

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area 2y=5sqrt(x),y=5,2y+4x=9

area

2 y = 5 x, y = 5, 2 y + 4 x = 9

\frac{235}{48}

Decimal

4.89583 \dots

Solution steps

Isolate

y

for

2 y = 5 x : y = \frac{5 x}{2}

Isolate

y

for

2 y + 4 x = 9 : y = \frac{9 - 4 x}{2}

f_{1} (x) = \frac{5 x}{2}

f_{2} (x) = 5

To find the intersection points solve

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

\frac{5 x}{2} = 5 : x = 4

\frac{5 x}{2} = \frac{9 - 4 x}{2} : x = 1

5 = \frac{9 - 4 x}{2} : x = - \frac{1}{4}

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

= \int_{- \frac{1}{4}}^{1} 5 - \frac{9 - 4 x}{2} d x + \int_{1}^{4} \frac{5 x}{2} - 5 d x

\int_{- \frac{1}{4}}^{1} 5 - \frac{9 - 4 x}{2} d x = \frac{25}{16}

\int_{1}^{4} \frac{5 x}{2} - 5 d x = \frac{10}{3}

= \frac{25}{16} + \frac{10}{3}

Simplify

= \frac{235}{48}

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What is area 2y=5sqrt(x),y=5,2y+4x=9 ?
The answer to area 2y=5sqrt(x),y=5,2y+4x=9 is 235/48