What is area y=x,y=-x+3,y=0 ?

The answer to area y=x,y=-x+3,y=0 is 9/4

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area y=x,y=-x+3,y=0

area

y = x, y = - x + 3, y = 0

\frac{9}{4}

Decimal Notation

2.25

Solution steps

To find the intersection points solve

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

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

x = 0 : x = 0

- x + 3 = 0 : x = 3

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

= \int_{0}^{\frac{3}{2}} ∣ x - 0 ∣ d x + \int_{\frac{3}{2}}^{3} ∣ 0 - (- x + 3) ∣ d x

\int_{0}^{\frac{3}{2}} ∣ x - 0 ∣ d x = \frac{9}{8}

\int_{\frac{3}{2}}^{3} ∣ 0 - (- x + 3) ∣ d x = \frac{9}{8}

= \frac{9}{8} + \frac{9}{8}

Simplify

= \frac{9}{4}

\int (sin^{2} (2 x)) d x

\frac{d y}{d x} = \frac{y ^{3}}{3 x - 2}

\int \frac{1}{2} x + 3 d x

x \to - 6 lim (\frac{2 x + 12}{x + 6})

x \to 0 lim (\frac{10}{x ( x + 1 )})