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

The integral from 0 to 1 of 2pixe^x is 2pi

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integral from 0 to 1 of 2pixe^x

\int_{0}^{1} 2 π x e^{x} d x

2 π

Decimal

6.28318 \dots

Solution steps

\int_{0}^{1} 2 π x e^{x} d x

Take the constant out:

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

= 2 π \cdot \int_{0}^{1} x e^{x} d x

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{0}^{1}

= 2 π [e^{x} x - \int e^{x} d x]_{0}^{1}

\int e^{x} d x = e^{x}

= 2 π [e^{x} x - e^{x}]_{0}^{1}

Compute the boundaries:

1

= 2 π 1

Simplify

= 2 π

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\int_{0}^{1} (\frac{6}{x ^{2} + 1}) d x

\int_{0}^{1} ∣ x (2 x - 1) ∣ d x

What is the integral from 0 to 1 of 2pixe^x ?
The integral from 0 to 1 of 2pixe^x is 2pi