What is the integral from-1 to 4 of (3x^4-5x^3-x-6) ?

The integral from-1 to 4 of (3x^4-5x^3-x-6) is 1035/4

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integral from-1 to 4 of (3x^4-5x^3-x-6)

\int_{- 1}^{4} (3 x^{4} - 5 x^{3} - x - 6) d x

\frac{1035}{4}

Decimal

258.75

Solution steps

\int_{- 1}^{4} 3 x^{4} - 5 x^{3} - x - 6 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} 3 x^{4} d x - \int_{- 1}^{4} 5 x^{3} d x - \int_{- 1}^{4} x d x - \int_{- 1}^{4} 6 d x

\int_{- 1}^{4} 3 x^{4} d x = 615

\int_{- 1}^{4} 5 x^{3} d x = \frac{1275}{4}

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

\int_{- 1}^{4} 6 d x = 30

= 615 - \frac{1275}{4} - \frac{15}{2} - 30

Simplify

615 - \frac{1275}{4} - \frac{15}{2} - 30 : \frac{1035}{4}

= \frac{1035}{4}

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What is the integral from-1 to 4 of (3x^4-5x^3-x-6) ?
The integral from-1 to 4 of (3x^4-5x^3-x-6) is 1035/4