What is the integral from 1 to 3 of (x^2+2x-5) ?

The integral from 1 to 3 of (x^2+2x-5) is 20/3

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integral from 1 to 3 of (x^2+2x-5)

\int_{1}^{3} (x^{2} + 2 x - 5) d x

\frac{20}{3}

Decimal Notation

6.66666 \dots

Solution steps

\int_{1}^{3} x^{2} + 2 x - 5 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}^{3} x^{2} d x + \int_{1}^{3} 2 x d x - \int_{1}^{3} 5 d x

\int_{1}^{3} x^{2} d x = \frac{26}{3}

\int_{1}^{3} 2 x d x = 8

\int_{1}^{3} 5 d x = 10

= \frac{26}{3} + 8 - 10

Simplify

\frac{26}{3} + 8 - 10 : \frac{20}{3}

= \frac{20}{3}

\frac{d}{d x} (\frac{e ^{x}}{3 x ^{2}})

x \to 0 lim (6 x^{2} (cot (3 x)) (csc (2 x)))

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

\int \frac{x - 1}{x ^{2} - 4 x + 3} d x

f (x) = - 2 x^{2}

What is the integral from 1 to 3 of (x^2+2x-5) ?
The integral from 1 to 3 of (x^2+2x-5) is 20/3