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Popular >

integral from 0 to 1 of (x+1)^2

Solution

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

Solution

\frac{7}{3}

+1

Decimal Notation

2.33333 \dots

Solution steps

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

Expand

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

= \int_{0}^{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_{0}^{1} x^{2} d x + \int_{0}^{1} 2 x d x + \int_{0}^{1} 1 d x

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

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

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

= \frac{1}{3} + 1 + 1

Simplify

\frac{1}{3} + 1 + 1 : \frac{7}{3}

= \frac{7}{3}

Popular Examples

integral from 0 to pi of tan^2(x)

\int_{0}^{π} tan^{2} (x) d x

derivative of (x^2-x+2/(sqrt(x)))

\frac{d}{d x} (\frac{x ^{2} - x + 2}{x})

area y=2x^2,y=16x-32,y=0 area

y = 2 x^{2}, y = 16 x - 32, y = 0

(dy)/(dt)=(y+1)/(t+1)

\frac{d y}{d t} = \frac{y + 1}{t + 1}

integral of 1/(sqrt(1-x^2))

\int \frac{1}{1 - x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of (x+1)^2 ?
The integral from 0 to 1 of (x+1)^2 is 7/3