What is area y=sqrt(2x),y=2x-12,y=0 ?

The answer to area y=sqrt(2x),y=2x-12,y=0 is 52/3

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area y=sqrt(2x),y=2x-12,y=0

area

y = 2 x, y = 2 x - 12, y = 0

\frac{52}{3}

Decimal

17.33333 \dots

Solution steps

To find the intersection points solve

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

2 x = 2 x - 12 : x = 8

2 x = 0 : x = 0

2 x - 12 = 0 : x = 6

= \int_{0}^{6} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{6}^{8} ∣ f_{2} (x) - f_{1} (x) ∣ d x

= \int_{0}^{6} 2 x - 0 d x + \int_{6}^{8} 2 x - 12 - 2 x d x

\int_{0}^{6} 2 x - 0 d x = 83

\int_{6}^{8} 2 x - 12 - 2 x d x = - 83 + \frac{52}{3}

= 83 - 83 + \frac{52}{3}

Simplify

= \frac{52}{3}

\frac{\partial}{\partial x} (2 x z)

\int \frac{1}{- t ^{2} + 8 t - 7} d t

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

y = x^{2} - x^{4} (1)

\frac{d}{d x} (2 x^{3} + \frac{2}{x ^{3}})

What is area y=sqrt(2x),y=2x-12,y=0 ?
The answer to area y=sqrt(2x),y=2x-12,y=0 is 52/3