What is the integral from 3 to 5 of x^2-8x+16 ?

The integral from 3 to 5 of x^2-8x+16 is 2/3

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integral from 3 to 5 of x^2-8x+16

\int_{3}^{5} x^{2} - 8 x + 16 d x

\frac{2}{3}

Decimal

0.66666 \dots

Solution steps

\int_{3}^{5} x^{2} - 8 x + 16 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

= \int_{3}^{5} x^{2} d x - \int_{3}^{5} 8 x d x + \int_{3}^{5} 16 d x

\int_{3}^{5} x^{2} d x = \frac{98}{3}

\int_{3}^{5} 8 x d x = 64

\int_{3}^{5} 16 d x = 32

= \frac{98}{3} - 64 + 32

Simplify

\frac{98}{3} - 64 + 32 : \frac{2}{3}

= \frac{2}{3}

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What is the integral from 3 to 5 of x^2-8x+16 ?
The integral from 3 to 5 of x^2-8x+16 is 2/3