What is area 2y=4sqrt(x),y=5,2y+3x=7 ?

The answer to area 2y=4sqrt(x),y=5,2y+3x=7 is 39/4

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area 2y=4sqrt(x),y=5,2y+3x=7

area

2 y = 4 x, y = 5, 2 y + 3 x = 7

\frac{39}{4}

Decimal Notation

9.75

Solution steps

Isolate

y

for

2 y = 4 x : y = 2 x

Isolate

y

for

2 y + 3 x = 7 : y = \frac{7 - 3 x}{2}

f_{1} (x) = 2 x

f_{2} (x) = 5

To find the intersection points solve

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

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

2 x = \frac{7 - 3 x}{2} : x = 1

5 = \frac{7 - 3 x}{2} : x = - 1

= \int_{- 1}^{1} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{1}^{\frac{25}{4}} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{- 1}^{1} 5 - \frac{7 - 3 x}{2} d x + \int_{1}^{\frac{25}{4}} 2 x - 5 d x

\int_{- 1}^{1} 5 - \frac{7 - 3 x}{2} d x = 3

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

= 3 + \frac{27}{4}

Simplify

= \frac{39}{4}

\frac{\partial}{\partial x} (\frac{53}{5 + x ^{2} + y ^{2}})

x \to 1 lim (sin (2 x))

\frac{d}{d x} (5 sin (π x))

\frac{d}{d x} (\frac{x ^{3}}{3} - 4 x + 1)

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 3 + e^{\frac{x}{2}}

What is area 2y=4sqrt(x),y=5,2y+3x=7 ?
The answer to area 2y=4sqrt(x),y=5,2y+3x=7 is 39/4