What is the integral from 1 to 2 of (3x^2-2x-1) ?

The integral from 1 to 2 of (3x^2-2x-1) is 3

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integral from 1 to 2 of (3x^2-2x-1)

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

3

Solution steps

\int_{1}^{2} 3 x^{2} - 2 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_{1}^{2} 3 x^{2} d x - \int_{1}^{2} 2 x d x - \int_{1}^{2} 1 d x

\int_{1}^{2} 3 x^{2} d x = 7

\int_{1}^{2} 2 x d x = 3

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

= 7 - 3 - 1

Simplify

= 3

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

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

\int_{0}^{4} (3 x + 4) d x

\int_{0}^{2} 2 x - x^{3} d x

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

What is the integral from 1 to 2 of (3x^2-2x-1) ?
The integral from 1 to 2 of (3x^2-2x-1) is 3