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Popular >

integral from 0 to 1 of x^2-x+1

Solution

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

Solution

\frac{5}{6}

+1

Decimal

0.83333 \dots

Solution steps

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

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

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

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

= \frac{1}{3} - \frac{1}{2} + 1

Simplify

\frac{1}{3} - \frac{1}{2} + 1 : \frac{5}{6}

= \frac{5}{6}

Graph

Popular Examples

integral from 1 to 3 of 3-x

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

integral from 1 to 3 of 3/(x(x+1))

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

integral from 0 to 1 of 3y^2

\int_{0}^{1} 3 y^{2} d y

integral from 0 to 1 of 1/(sqrt(2x-x^2))

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

integral from-3 to-1 of 1/(x^2-6x+25)

\int_{- 3}^{- 1} \frac{1}{x ^{2} - 6 x + 25} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of x^2-x+1 ?
The integral from 0 to 1 of x^2-x+1 is 5/6