What is the integral from 0 to a of (3x^2-x+1) ?

The integral from 0 to a of (3x^2-x+1) is a^3-(a^2)/2+a

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integral from 0 to a of (3x^2-x+1)

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

a^{3} - \frac{a ^{2}}{2} + a

Solution steps

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

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

\int_{0}^{a} x d x = \frac{a ^{2}}{2}

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

= a^{3} - \frac{a ^{2}}{2} + a

\int_{0}^{0.3} 3 e^{- x^{2}} d x

\int_{0}^{2} x 2 x^{2} + 1 d x

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

\int_{7}^{0} ∣ 2 x - 7 ∣ d x

\int_{0}^{3} 2 x 9 - x^{2} d x

What is the integral from 0 to a of (3x^2-x+1) ?
The integral from 0 to a of (3x^2-x+1) is a^3-(a^2)/2+a