What is the integral from 3 to 10 of (100-y^2)(y+2) ?

The integral from 3 to 10 of (100-y^2)(y+2) is 33859/12

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integral from 3 to 10 of (100-y^2)(y+2)

\int_{3}^{10} (100 - y^{2}) (y + 2) d y

\frac{33859}{12}

Decimal Notation

2821.58333 \dots

Solution steps

\int_{3}^{10} (100 - y^{2}) (y + 2) d y

Expand

(100 - y^{2}) (y + 2) : 100 y + 200 - y^{3} - 2 y^{2}

= \int_{3}^{10} 100 y + 200 - y^{3} - 2 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_{3}^{10} 100 y d y + \int_{3}^{10} 200 d y - \int_{3}^{10} y^{3} d y - \int_{3}^{10} 2 y^{2} d y

\int_{3}^{10} 100 y d y = 4550

\int_{3}^{10} 200 d y = 1400

\int_{3}^{10} y^{3} d y = \frac{9919}{4}

\int_{3}^{10} 2 y^{2} d y = \frac{1946}{3}

= 4550 + 1400 - \frac{9919}{4} - \frac{1946}{3}

Simplify

4550 + 1400 - \frac{9919}{4} - \frac{1946}{3} : \frac{33859}{12}

= \frac{33859}{12}

f (x) = x^{3} - 5

\frac{d}{d x} (\frac{1}{x ^{4} + x ^{2} + 1})

\frac{d y}{d x} = \frac{( 2 x ^{4} + 2 y )}{- 2 x - 3 y}

- 2 sin (2 t)

\int \frac{4}{3 + 4 x} d x

What is the integral from 3 to 10 of (100-y^2)(y+2) ?
The integral from 3 to 10 of (100-y^2)(y+2) is 33859/12