What is the integral from-1 to 4 of (x^2+2x-1) ?

The integral from-1 to 4 of (x^2+2x-1) is 95/3

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integral from-1 to 4 of (x^2+2x-1)

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

\frac{95}{3}

Decimal

31.66666 \dots

Solution steps

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

\int_{- 1}^{4} x^{2} d x = \frac{65}{3}

\int_{- 1}^{4} 2 x d x = 15

\int_{- 1}^{4} 1 d x = 5

= \frac{65}{3} + 15 - 5

Simplify

\frac{65}{3} + 15 - 5 : \frac{95}{3}

= \frac{95}{3}

What is the integral from-1 to 4 of (x^2+2x-1) ?
The integral from-1 to 4 of (x^2+2x-1) is 95/3