What is the integral from 5 to 6 of c(36-x^2) ?

The integral from 5 to 6 of c(36-x^2) is 17/3 c

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integral from 5 to 6 of c(36-x^2)

\int_{5}^{6} c (36 - x^{2}) d x

\frac{17}{3} c

Solution steps

\int_{5}^{6} c (36 - x^{2}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= c \cdot \int_{5}^{6} 36 - x^{2} 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

= c (\int_{5}^{6} 36 d x - \int_{5}^{6} x^{2} d x)

\int_{5}^{6} 36 d x = 36

\int_{5}^{6} x^{2} d x = \frac{91}{3}

= c (36 - \frac{91}{3})

Join

36 - \frac{91}{3} : \frac{17}{3}

= \frac{17}{3} c

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What is the integral from 5 to 6 of c(36-x^2) ?
The integral from 5 to 6 of c(36-x^2) is 17/3 c