What is the integral from 3 to 4 of-x^3+7x^2-12x ?

The integral from 3 to 4 of-x^3+7x^2-12x is 7/12

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integral from 3 to 4 of-x^3+7x^2-12x

\int_{3}^{4} - x^{3} + 7 x^{2} - 12 x d x

\frac{7}{12}

Decimal

0.58333 \dots

Solution steps

\int_{3}^{4} - x^{3} + 7 x^{2} - 12 x 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_{3}^{4} x^{3} d x + \int_{3}^{4} 7 x^{2} d x - \int_{3}^{4} 12 x d x

\int_{3}^{4} x^{3} d x = \frac{175}{4}

\int_{3}^{4} 7 x^{2} d x = \frac{259}{3}

\int_{3}^{4} 12 x d x = 42

= - \frac{175}{4} + \frac{259}{3} - 42

Simplify

- \frac{175}{4} + \frac{259}{3} - 42 : \frac{7}{12}

= \frac{7}{12}

\int_{0}^{\infty} x ln (x) d x

\int_{0}^{1} (8 x^{e} + 7 e^{x}) d x

\int_{- 5}^{0} 0 d x

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

\int_{0}^{8} \frac{1}{2} x d x

What is the integral from 3 to 4 of-x^3+7x^2-12x ?
The integral from 3 to 4 of-x^3+7x^2-12x is 7/12