What is the integral from-1 to 4 of (2x^4+2x^3-x-7) ?

The integral from-1 to 4 of (2x^4+2x^3-x-7) is 495

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integral from-1 to 4 of (2x^4+2x^3-x-7)

\int_{- 1}^{4} (2 x^{4} + 2 x^{3} - x - 7) d x

495

Solution steps

\int_{- 1}^{4} 2 x^{4} + 2 x^{3} - 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_{- 1}^{4} 2 x^{4} d x + \int_{- 1}^{4} 2 x^{3} d x - \int_{- 1}^{4} x d x - \int_{- 1}^{4} 7 d x

\int_{- 1}^{4} 2 x^{4} d x = 410

\int_{- 1}^{4} 2 x^{3} d x = \frac{255}{2}

\int_{- 1}^{4} x d x = \frac{15}{2}

\int_{- 1}^{4} 7 d x = 35

= 410 + \frac{255}{2} - \frac{15}{2} - 35

Simplify

410 + \frac{255}{2} - \frac{15}{2} - 35 : 495

= 495

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What is the integral from-1 to 4 of (2x^4+2x^3-x-7) ?
The integral from-1 to 4 of (2x^4+2x^3-x-7) is 495