What is the integral from 4 to 6 of (x^2+2x-7) ?

The integral from 4 to 6 of (x^2+2x-7) is 170/3

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integral from 4 to 6 of (x^2+2x-7)

\int_{4}^{6} (x^{2} + 2 x - 7) d x

\frac{170}{3}

Decimal

56.66666 \dots

Solution steps

\int_{4}^{6} x^{2} + 2 x - 7 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_{4}^{6} x^{2} d x + \int_{4}^{6} 2 x d x - \int_{4}^{6} 7 d x

\int_{4}^{6} x^{2} d x = \frac{152}{3}

\int_{4}^{6} 2 x d x = 20

\int_{4}^{6} 7 d x = 14

= \frac{152}{3} + 20 - 14

Simplify

\frac{152}{3} + 20 - 14 : \frac{170}{3}

= \frac{170}{3}

\int_{\frac{3 π}{2}}^{π} x cos (x) d x

\int_{4}^{6} (x^{2} + 2 x - 6) d x

\int_{0}^{10} x e^{1 - x^{2}} d x

\int_{0}^{2 π} t cos (t) d t

\int_{0}^{1} ln^{2} (x) d x

What is the integral from 4 to 6 of (x^2+2x-7) ?
The integral from 4 to 6 of (x^2+2x-7) is 170/3