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

The integral from-2 to 3 of (2x^4+2x^3-x+7) is 175

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

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

175

Solution steps

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

\int_{- 2}^{3} 2 x^{4} d x = 110

\int_{- 2}^{3} 2 x^{3} d x = \frac{65}{2}

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

\int_{- 2}^{3} 7 d x = 35

= 110 + \frac{65}{2} - \frac{5}{2} + 35

Simplify

110 + \frac{65}{2} - \frac{5}{2} + 35 : 175

= 175

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What is the integral from-2 to 3 of (2x^4+2x^3-x+7) ?
The integral from-2 to 3 of (2x^4+2x^3-x+7) is 175