What is the integral from 1 to 2 of 64/3-8y^2 ?

The integral from 1 to 2 of 64/3-8y^2 is 8/3

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integral from 1 to 2 of 64/3-8y^2

\int_{1}^{2} \frac{64}{3} - 8 y^{2} d y

\frac{8}{3}

Decimal

2.66666 \dots

Solution steps

\int_{1}^{2} \frac{64}{3} - 8 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}^{2} \frac{64}{3} d y - \int_{1}^{2} 8 y^{2} d y

\int_{1}^{2} \frac{64}{3} d y = \frac{64}{3}

\int_{1}^{2} 8 y^{2} d y = \frac{56}{3}

= \frac{64}{3} - \frac{56}{3}

Simplify

\frac{64}{3} - \frac{56}{3} : \frac{8}{3}

= \frac{8}{3}

What is the integral from 1 to 2 of 64/3-8y^2 ?
The integral from 1 to 2 of 64/3-8y^2 is 8/3