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Popular Calculus >

integral from-1 to 3 of x^2-2x+3

Solution

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

Solution

\frac{40}{3}

+1

Decimal

13.33333 \dots

Solution steps

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

\int_{- 1}^{3} x^{2} d x = \frac{28}{3}

\int_{- 1}^{3} 2 x d x = 8

\int_{- 1}^{3} 3 d x = 12

= \frac{28}{3} - 8 + 12

Simplify

\frac{28}{3} - 8 + 12 : \frac{40}{3}

= \frac{40}{3}

Graph

Popular Examples

integral from 2 to 5 of (sqrt(x)+5)

\int_{2}^{5} (x + 5) d x

integral from 0 to 3 of sqrt(3^2-x^2)

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

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

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

integral from 0 to 1 of x(6x(1-x))

\int_{0}^{1} x (6 x (1 - x)) d x

integral from-3 to 6 of 6-x^2

\int_{- 3}^{6} 6 - x^{2} d x

Frequently Asked Questions (FAQ)

What is the integral from-1 to 3 of x^2-2x+3 ?
The integral from-1 to 3 of x^2-2x+3 is 40/3