What is the integral from-4 to 5 of 8-y-((y-2)^2)/3 ?

The integral from-4 to 5 of 8-y-((y-2)^2)/3 is 81/2

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integral from-4 to 5 of 8-y-((y-2)^2)/3

\int_{- 4}^{5} 8 - y - \frac{( y - 2 ) ^{2}}{3} d y

\frac{81}{2}

Decimal

40.5

Solution steps

\int_{- 4}^{5} 8 - y - \frac{( y - 2 ) ^{2}}{3} 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_{- 4}^{5} 8 d y - \int_{- 4}^{5} y d y - \int_{- 4}^{5} \frac{( y - 2 ) ^{2}}{3} d y

\int_{- 4}^{5} 8 d y = 72

\int_{- 4}^{5} y d y = \frac{9}{2}

\int_{- 4}^{5} \frac{( y - 2 ) ^{2}}{3} d y = 27

= 72 - \frac{9}{2} - 27

Simplify

72 - \frac{9}{2} - 27 : \frac{81}{2}

= \frac{81}{2}

What is the integral from-4 to 5 of 8-y-((y-2)^2)/3 ?
The integral from-4 to 5 of 8-y-((y-2)^2)/3 is 81/2