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Popular >

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

Solution

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

Solution

\frac{8}{3}

+1

Decimal

2.66666 \dots

Solution steps

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

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

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

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

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

Simplify

\frac{2}{3} + 0 + 2 : \frac{8}{3}

= \frac{8}{3}

Graph

Popular Examples

integral from-8 to-1 of 1-\sqrt[3]{x}

\int_{- 8}^{- 1} 1 - 3 x d x

integral from 1 to e of (2ln|x|)/x

\int_{1}^{e} \frac{2 ln ∣ x ∣}{x} d x

integral from 0 to t of (sin(x))/x

\int_{0}^{t} \frac{sin ( x )}{x} d x

integral from 1 to 3 of (x+y^2)

\int_{1}^{3} (x + y^{2}) d x

integral from 2 to 6 of x/(sqrt(x-2))

\int_{2}^{6} \frac{x}{x - 2} d x

Frequently Asked Questions (FAQ)

What is the integral from-1 to 1 of x^2+2x+1 ?
The integral from-1 to 1 of x^2+2x+1 is 8/3