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Popular >

integral from-1 to 1 of x^2-x-1

Solution

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

Solution

- \frac{4}{3}

+1

Decimal Notation

- 1.33333 \dots

Solution steps

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

\int_{- 1}^{1} x^{2} d x = \frac{2}{3}

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

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

= \frac{2}{3} - 0 - 2

Simplify

\frac{2}{3} - 0 - 2 : - \frac{4}{3}

= - \frac{4}{3}

Popular Examples

(\frac{4}{3})^{^{'}}

derivative of ln(5x^2+3y^2)

\frac{d}{d x} (ln (5 x^{2} + 3 y^{2}))

(1 + e^{2 x})^{^{'}}

d/(dy)(y^3+xy^2+y)

\frac{d}{d y} (y^{3} + x y^{2} + y)

limit as x approaches (2pi)/3 of-tan(2x)

x \to \frac{2 π}{3} lim (- tan (2 x))

Frequently Asked Questions (FAQ)

What is the integral from-1 to 1 of x^2-x-1 ?
The integral from-1 to 1 of x^2-x-1 is -4/3