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Popular >

integral from-1 to 0 of |x|-1

Solution

\int_{- 1}^{0} ∣ x ∣ - 1 d x

Solution

- \frac{1}{2}

+1

Decimal

- 0.5

Solution steps

\int_{- 1}^{0} ∣ x ∣ - 1 d x

Eliminate Absolutes

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

= - (- \frac{1}{2}) - 1

Simplify

- (- \frac{1}{2}) - 1 : - \frac{1}{2}

= - \frac{1}{2}

Graph

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\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) - 3 d x

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

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

Frequently Asked Questions (FAQ)

What is the integral from-1 to 0 of |x|-1 ?
The integral from-1 to 0 of |x|-1 is -1/2