What is the integral from 6 to 7 of 13x-x^2-42 ?

The integral from 6 to 7 of 13x-x^2-42 is 1/6

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integral from 6 to 7 of 13x-x^2-42

\int_{6}^{7} 13 x - x^{2} - 42 d x

\frac{1}{6}

Decimal

0.16666 \dots

Solution steps

\int_{6}^{7} 13 x - x^{2} - 42 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_{6}^{7} 13 x d x - \int_{6}^{7} x^{2} d x - \int_{6}^{7} 42 d x

\int_{6}^{7} 13 x d x = \frac{169}{2}

\int_{6}^{7} x^{2} d x = \frac{127}{3}

\int_{6}^{7} 42 d x = 42

= \frac{169}{2} - \frac{127}{3} - 42

Simplify

\frac{169}{2} - \frac{127}{3} - 42 : \frac{1}{6}

= \frac{1}{6}

What is the integral from 6 to 7 of 13x-x^2-42 ?
The integral from 6 to 7 of 13x-x^2-42 is 1/6