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Popular Calculus >

area x^3,-x,1

Solution

area

x^{3}, - x, 1

Solution

\frac{5}{4}

+1

Decimal

1.25

Solution steps

To find the intersection points solve

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

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

x^{3} = 1 : x = 1

- x = 1 : x = - 1

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

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

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

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

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

Simplify

= \frac{5}{4}

Graph

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Frequently Asked Questions (FAQ)

What is area x^3,-x,1 ?
The answer to area x^3,-x,1 is 5/4