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Popular >

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

Solution

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

Solution

\frac{8}{3}

+1

Decimal Notation

2.66666 \dots

Solution steps

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

Expand

(x + 1)^{2} : x^{2} + 2 x + 1

= \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}

Popular Examples

integral of 700xsqrt(3+2x)

\int 700 x 3 + 2 x d x

integral from 0 to 2 of x^3

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

integral from 1 to 3 of 7/(x^2)

\int_{1}^{3} \frac{7}{x ^{2}} d x

d/(dt)(y+{v}(t)*t+(a/2)*t^2)

\frac{d}{d t} (y + v (t) \cdot t + (\frac{a}{2}) \cdot t^{2})

integral from 0 to 2 of xsqrt(2-x)

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

Frequently Asked Questions (FAQ)

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