What is the integral from-2 to 3 of (3x^4-5x^3-x-6) ?

The integral from-2 to 3 of (3x^4-5x^3-x-6) is 205/4

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integral from-2 to 3 of (3x^4-5x^3-x-6)

\int_{- 2}^{3} (3 x^{4} - 5 x^{3} - x - 6) d x

\frac{205}{4}

Decimal

51.25

Solution steps

\int_{- 2}^{3} 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_{- 2}^{3} 3 x^{4} d x - \int_{- 2}^{3} 5 x^{3} d x - \int_{- 2}^{3} x d x - \int_{- 2}^{3} 6 d x

\int_{- 2}^{3} 3 x^{4} d x = 165

\int_{- 2}^{3} 5 x^{3} d x = \frac{325}{4}

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

\int_{- 2}^{3} 6 d x = 30

= 165 - \frac{325}{4} - \frac{5}{2} - 30

Simplify

165 - \frac{325}{4} - \frac{5}{2} - 30 : \frac{205}{4}

= \frac{205}{4}

\int_{0}^{1} x \cdot 1 + x^{2} d x

\int_{1}^{2} (- x^{2} + 5) d x

\int_{0}^{1} \frac{2 x ^{3}}{x ^{2} + x} d x

\int_{x}^{1} e^{- y^{2}} d y

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

What is the integral from-2 to 3 of (3x^4-5x^3-x-6) ?
The integral from-2 to 3 of (3x^4-5x^3-x-6) is 205/4