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Popular >

integral from 0 to 3 of 3x^2-4x+1

Solution

\int_{0}^{3} 3 x^{2} - 4 x + 1 d x

Solution

12

Solution steps

\int_{0}^{3} 3 x^{2} - 4 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_{0}^{3} 3 x^{2} d x - \int_{0}^{3} 4 x d x + \int_{0}^{3} 1 d x

\int_{0}^{3} 3 x^{2} d x = 27

\int_{0}^{3} 4 x d x = 18

\int_{0}^{3} 1 d x = 3

= 27 - 18 + 3

Simplify

= 12

Graph

Popular Examples

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\int_{0}^{1} (x^{4} - x^{3}) d x

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\int_{0}^{8} \frac{12}{x + 1} d x

integral from 21 to x of 1/t

\int_{21}^{x} \frac{1}{t} d t

integral from pi to 0 of sin^4(x)

\int_{π}^{0} sin^{4} (x) d x

integral from 1 to 2 of (-4t^{-4})

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

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of 3x^2-4x+1 ?
The integral from 0 to 3 of 3x^2-4x+1 is 12