What is the integral from-1 to 22 of 21x-(x^2-22) ?

The integral from-1 to 22 of 21x-(x^2-22) is 12167/6

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integral from-1 to 22 of 21x-(x^2-22)

\int_{- 1}^{22} 21 x - (x^{2} - 22) d x

\frac{12167}{6}

Decimal Notation

2027.83333 \dots

Solution steps

\int_{- 1}^{22} 21 x - (x^{2} - 22) d x

Simplify

= \int_{- 1}^{22} 21 x - x^{2} + 22 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_{- 1}^{22} 21 x d x - \int_{- 1}^{22} x^{2} d x + \int_{- 1}^{22} 22 d x

\int_{- 1}^{22} 21 x d x = \frac{10143}{2}

\int_{- 1}^{22} x^{2} d x = \frac{10649}{3}

\int_{- 1}^{22} 22 d x = 506

= \frac{10143}{2} - \frac{10649}{3} + 506

Simplify

\frac{10143}{2} - \frac{10649}{3} + 506 : \frac{12167}{6}

= \frac{12167}{6}

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What is the integral from-1 to 22 of 21x-(x^2-22) ?
The integral from-1 to 22 of 21x-(x^2-22) is 12167/6