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

The integral from 0 to 1 of pi(e^x+3x) is pi(e+1/2)

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integral from 0 to 1 of pi(e^x+3x)

\int_{0}^{1} π (e^{x} + 3 x) d x

π (e + \frac{1}{2})

Decimal

10.11053 \dots

Solution steps

\int_{0}^{1} π (e^{x} + 3 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= π \cdot \int_{0}^{1} e^{x} + 3 x 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

= π (\int_{0}^{1} e^{x} d x + \int_{0}^{1} 3 x d x)

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

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

= π (e - 1 + \frac{3}{2})

Combine the fractions

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

= π (e + \frac{1}{2})

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