What is area Y=(x^{1/2}),Y=6-x,Y=0 ?

The answer to area Y=(x^{1/2}),Y=6-x,Y=0 is 22/3

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area Y=(x^{1/2}),Y=6-x,Y=0

area

Y = (x^{\frac{1}{2}}), Y = 6 - x, Y = 0

\frac{22}{3}

Decimal

7.33333 \dots

Solution steps

To find the intersection points solve

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

(x^{\frac{1}{2}}) = 6 - x : x = 4

(x^{\frac{1}{2}}) = 0 : x = 0

6 - x = 0 : x = 6

= \int_{0}^{4} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{4}^{6} ∣ f_{3} (x) - f_{2} (x) ∣ d x

= \int_{0}^{4} (x^{\frac{1}{2}}) - 0 d x + \int_{4}^{6} ∣ 0 - (6 - x) ∣ d x

\int_{0}^{4} (x^{\frac{1}{2}}) - 0 d x = \frac{16}{3}

\int_{4}^{6} ∣ 0 - (6 - x) ∣ d x = 2

= \frac{16}{3} + 2

Simplify

= \frac{22}{3}

\int e^{x - 3} d x

e^{x}, e^{- 3 x}, x = ln (4)

\int \frac{x ^{2} - 2}{x} d x

\frac{150000}{( 4 x + 75 ) ^{2}}

π^{7} + 3 x

What is area Y=(x^{1/2}),Y=6-x,Y=0 ?
The answer to area Y=(x^{1/2}),Y=6-x,Y=0 is 22/3