Evaluate using formulas and rules of \int _0^2(3x^2+x-1)

Solve int _0^2(3x^2+x-1)

Evaluate

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

Evaluate the integral

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

Use the property of integral \int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

\int 3 x^{2} d x + \int x d x + \int - 1 d x

Evaluate the integral

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x^{3} + \int x d x + \int - 1 d x

Evaluate the integral

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x^{3} + \frac{x ^{2}}{2} + \int - 1 d x

Use the property of integral \int k d x = k x

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

Return the limits

(x^{3} + \frac{x ^{2}}{2} - x)_{0}^{2}

Solution

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8