What is area 2y=5sqrt(x),y=4,2y+3x=8 ?

The answer to area 2y=5sqrt(x),y=4,2y+3x=8 is 183/100

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area 2y=5sqrt(x),y=4,2y+3x=8

area

2 y = 5 x, y = 4, 2 y + 3 x = 8

\frac{183}{100}

Decimal

1.83

Solution steps

Isolate

y

for

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

Isolate

y

for

2 y + 3 x = 8 : y = \frac{8 - 3 x}{2}

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

f_{2} (x) = 4

To find the intersection points solve

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

\frac{5 x}{2} = 4 : x = \frac{64}{25}

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

4 = \frac{8 - 3 x}{2} : x = 0

= \int_{0}^{1} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{1}^{\frac{64}{25}} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{0}^{1} 4 - \frac{8 - 3 x}{2} d x + \int_{1}^{\frac{64}{25}} \frac{5 x}{2} - 4 d x

\int_{0}^{1} 4 - \frac{8 - 3 x}{2} d x = \frac{3}{4}

\int_{1}^{\frac{64}{25}} \frac{5 x}{2} - 4 d x = \frac{27}{25}

= \frac{3}{4} + \frac{27}{25}

Simplify

= \frac{183}{100}

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

y = - csc (x) - sin (x)

y^{^{''}} - 4 y^{^{'}} - 5 y = - 3 e^{4} t, y (0) = 0, y^{^{'}} (0) = 0

\int_{1}^{x} (\frac{1}{t ^{3} + 1}) d t

\int \frac{1}{sec ( a x ) + 1} d x

What is area 2y=5sqrt(x),y=4,2y+3x=8 ?
The answer to area 2y=5sqrt(x),y=4,2y+3x=8 is 183/100