What is the integral from 2 to 4 of (6x^2-6x-1) ?

The integral from 2 to 4 of (6x^2-6x-1) is 74

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integral from 2 to 4 of (6x^2-6x-1)

\int_{2}^{4} (6 x^{2} - 6 x - 1) d x

74

Solution steps

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

\int_{2}^{4} 6 x^{2} d x = 112

\int_{2}^{4} 6 x d x = 36

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

= 112 - 36 - 2

Simplify

= 74

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

\int_{0}^{1} t e^{\frac{t ^{2}}{2}} d t

\int_{0}^{1} 3 x (1 - x)^{2} d x

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

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

What is the integral from 2 to 4 of (6x^2-6x-1) ?
The integral from 2 to 4 of (6x^2-6x-1) is 74