What is the integral from 1 to 4 of (2-9x-4x^2) ?

The integral from 1 to 4 of (2-9x-4x^2) is -291/2

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integral from 1 to 4 of (2-9x-4x^2)

\int_{1}^{4} (2 - 9 x - 4 x^{2}) d x

- \frac{291}{2}

Decimal

- 145.5

Solution steps

\int_{1}^{4} 2 - 9 x - 4 x^{2} 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 d x - \int_{1}^{4} 9 x d x - \int_{1}^{4} 4 x^{2} d x

\int_{1}^{4} 2 d x = 6

\int_{1}^{4} 9 x d x = \frac{135}{2}

\int_{1}^{4} 4 x^{2} d x = 84

= 6 - \frac{135}{2} - 84

Simplify

6 - \frac{135}{2} - 84 : - \frac{291}{2}

= - \frac{291}{2}

\int_{0}^{1} x e^{- 9 x} d x

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What is the integral from 1 to 4 of (2-9x-4x^2) ?
The integral from 1 to 4 of (2-9x-4x^2) is -291/2