What is area ((3sqrt(x)))/2 ,3,2-(1/2 x) ?

The answer to area ((3sqrt(x)))/2 ,3,2-(1/2 x) is 17/4

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area ((3sqrt(x)))/2 ,3,2-(1/2 x)

area

\frac{( 3 x )}{2}, 3, 2 - (\frac{1}{2} x)

\frac{17}{4}

Decimal Notation

4.25

Solution steps

To find the intersection points solve

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

\frac{( 3 x )}{2} = 2 - (\frac{1}{2} x) : x = 1

\frac{( 3 x )}{2} = 3 : x = 4

2 - (\frac{1}{2} x) = 3 : x = - 2

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

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

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

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

= \frac{9}{4} + 2

Simplify

= \frac{17}{4}

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What is area ((3sqrt(x)))/2 ,3,2-(1/2 x) ?
The answer to area ((3sqrt(x)))/2 ,3,2-(1/2 x) is 17/4