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Popular >

area y^2-2x=7,x-y=4

Solution

area

y^{2} - 2 x = 7, x - y = 4

Solution

\frac{128}{3}

+1

Decimal Notation

42.66666 \dots

Solution steps

Isolate

y

for

y^{2} - 2 x = 7 : y = 7 + 2 x, y = - 7 + 2 x

Isolate

y

for

x - y = 4 : y = - 4 + x

f_{1} (x) = 7 + 2 x

f_{2} (x) = - 7 + 2 x

To find the intersection points solve

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

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

7 + 2 x = - 4 + x : x = 9

- 7 + 2 x = - 4 + x : x = 1

= \int_{- \frac{7}{2}}^{1} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{1}^{9} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- \frac{7}{2}}^{1} 7 + 2 x - (- 7 + 2 x) d x + \int_{1}^{9} 7 + 2 x - (- 4 + x) d x

\int_{- \frac{7}{2}}^{1} 7 + 2 x - (- 7 + 2 x) d x = 18

\int_{1}^{9} 7 + 2 x - (- 4 + x) d x = \frac{74}{3}

= 18 + \frac{74}{3}

Simplify

= \frac{128}{3}

Popular Examples

derivative of x^5*e^x derivative of

x^{5} \cdot e^{x}

area y=|x-12|,y= x/3 area

y = ∣ x - 12 ∣, y = \frac{x}{3}

tangent of f(x)=x^3-x^2+3 tangent of

f (x) = x^{3} - x^{2} + 3

maclaurin (1+x)^{1/2}maclaurin

(1 + x)^{\frac{1}{2}}

(\partial)/(\partial x)(10xy)

\frac{\partial}{\partial x} (10 x y)

Frequently Asked Questions (FAQ)

What is area y^2-2x=7,x-y=4 ?
The answer to area y^2-2x=7,x-y=4 is 128/3