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Popular Calculus >

integral from-1 to 3 of 8+2y-y^2

Solution

\int_{- 1}^{3} 8 + 2 y - y^{2} d y

Solution

\frac{92}{3}

+1

Decimal

30.66666 \dots

Solution steps

\int_{- 1}^{3} 8 + 2 y - y^{2} d y

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} 8 d y + \int_{- 1}^{3} 2 y d y - \int_{- 1}^{3} y^{2} d y

\int_{- 1}^{3} 8 d y = 32

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

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

= 32 + 8 - \frac{28}{3}

Simplify

32 + 8 - \frac{28}{3} : \frac{92}{3}

= \frac{92}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from-1 to 3 of 8+2y-y^2 ?
The integral from-1 to 3 of 8+2y-y^2 is 92/3