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Popular Calculus >

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

Solution

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

Solution

\frac{32}{3}

+1

Decimal

10.66666 \dots

Solution steps

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

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

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

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

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

Simplify

8 - \frac{28}{3} + 12 : \frac{32}{3}

= \frac{32}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from-1 to 3 of 2x-x^2+3 ?
The integral from-1 to 3 of 2x-x^2+3 is 32/3