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Popular >

integral from-1 to 1 of sqrt(x^2)

Solution

\int_{- 1}^{1} x^{2} d x

Solution

1

Solution steps

\int_{- 1}^{1} x^{2} d x

Apply exponent rule:

a^{2} = ∣ a ∣

= \int_{- 1}^{1} ∣ x ∣ d x

Eliminate Absolutes

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

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

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

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

Simplify

\frac{1}{2} + \frac{1}{2} : 1

= 1

Popular Examples

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\int_{0}^{1} (2 - x) e^{x} d x

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\int_{0}^{1} \frac{4 x}{3} + y^{2} d y

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\int_{- 1}^{5} 1 d x

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\int_{0}^{π} (10 sin (x)) d x

integral from 1 to 2 of 4/x

\int_{1}^{2} \frac{4}{x} d x

Frequently Asked Questions (FAQ)

What is the integral from-1 to 1 of sqrt(x^2) ?
The integral from-1 to 1 of sqrt(x^2) is 1