What is area x^3+1,-x+1,y=0 ?

The answer to area x^3+1,-x+1,y=0 is 5/4

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area x^3+1,-x+1,y=0

area

x^{3} + 1, - x + 1, y = 0

\frac{5}{4}

Decimal Notation

1.25

Solution steps

To find the intersection points solve

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

0 = x^{3} + 1 : x = - 1

0 = - x + 1 : x = 1

x^{3} + 1 = - x + 1 : x = 0

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

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

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

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

= \frac{3}{4} + \frac{1}{2}

Simplify

= \frac{5}{4}

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