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Popular Calculus >

area x^2,2x-1,0

Solution

area

x^{2}, 2 x - 1, 0

Solution

\frac{1}{12}

+1

Decimal

0.08333 \dots

Solution steps

To find the intersection points solve

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

x^{2} = 2 x - 1 : x = 1

x^{2} = 0 : x = 0

2 x - 1 = 0 : x = \frac{1}{2}

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

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

\int_{0}^{\frac{1}{2}} x^{2} - 0 d x = \frac{1}{24}

\int_{\frac{1}{2}}^{1} 2 x - 1 - x^{2} d x = \frac{1}{24}

= \frac{1}{24} + \frac{1}{24}

Simplify

= \frac{1}{12}

Graph

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Frequently Asked Questions (FAQ)

What is area x^2,2x-1,0 ?
The answer to area x^2,2x-1,0 is 1/12