What is the integral from 0 to 1 of (e^x+3x-5x^2) ?

The integral from 0 to 1 of (e^x+3x-5x^2) is e-7/6

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integral from 0 to 1 of (e^x+3x-5x^2)

\int_{0}^{1} (e^{x} + 3 x - 5 x^{2}) d x

e - \frac{7}{6}

Decimal Notation

1.55161 \dots

Solution steps

\int_{0}^{1} e^{x} + 3 x - 5 x^{2} 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}^{1} e^{x} d x + \int_{0}^{1} 3 x d x - \int_{0}^{1} 5 x^{2} d x

\int_{0}^{1} e^{x} d x = e - 1

\int_{0}^{1} 3 x d x = \frac{3}{2}

\int_{0}^{1} 5 x^{2} d x = \frac{5}{3}

= e - 1 + \frac{3}{2} - \frac{5}{3}

Combine the fractions

- 1 + \frac{3}{2} - \frac{5}{3} : - \frac{7}{6}

= e - \frac{7}{6}

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What is the integral from 0 to 1 of (e^x+3x-5x^2) ?
The integral from 0 to 1 of (e^x+3x-5x^2) is e-7/6