What is the integral from 0 to 1 of e^x+x^2 ?

The integral from 0 to 1 of e^x+x^2 is e-2/3

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integral from 0 to 1 of e^x+x^2

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

e - \frac{2}{3}

Decimal

2.05161 \dots

Solution steps

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

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

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

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

Combine the fractions

- 1 + \frac{1}{3} : - \frac{2}{3}

= e - \frac{2}{3}

\int_{- \infty}^{0} \frac{1}{e ^{x} + 1} d x

\int_{0}^{1 - x} x - x^{2} - x y d y

\int_{2}^{5} (x) d x

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

\int_{7}^{2} 1 d x

What is the integral from 0 to 1 of e^x+x^2 ?
The integral from 0 to 1 of e^x+x^2 is e-2/3