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

The integral from 0 to 4 of x^2+2x-3 is 76/3

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

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

\frac{76}{3}

Solution steps

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

\int_{0}^{4} x^{2} d x = \frac{64}{3}

\int_{0}^{4} 2 x d x = 16

\int_{0}^{4} 3 d x = 12

= \frac{64}{3} + 16 - 12

Simplify

\frac{64}{3} + 16 - 12 : \frac{76}{3}

= \frac{76}{3}

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What is the integral from 0 to 4 of x^2+2x-3 ?
The integral from 0 to 4 of x^2+2x-3 is 76/3