What is the integral from 0 to pi of 2pixsin(x) ?

The integral from 0 to pi of 2pixsin(x) is 2pi^2

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integral from 0 to pi of 2pixsin(x)

\int_{0}^{π} 2 π x sin (x) d x

2 π^{2}

Decimal

19.73920 \dots

Solution steps

\int_{0}^{π} 2 π x sin (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}^{π} x sin (x) d x

Apply Integration By Parts

: [- x cos (x) - \int - cos (x) d x]_{0}^{π}

= 2 π [- x cos (x) - \int - cos (x) d x]_{0}^{π}

\int - cos (x) d x = - sin (x)

= 2 π [- x cos (x) - (- sin (x))]_{0}^{π}

Simplify

= 2 π [- x cos (x) + sin (x)]_{0}^{π}

Compute the boundaries:

π

= 2 ππ

Simplify

= 2 π^{2}

\frac{\partial}{\partial x} ((x y)^{5})

\frac{d}{d x} (x^{2} \cdot I n (x))

f (x) = (1 + 2 x) (6 - 5 x), at x = 1

\frac{\partial}{\partial x} (2 ln (x y))

\int x^{2} arcsin (x) d x

What is the integral from 0 to pi of 2pixsin(x) ?
The integral from 0 to pi of 2pixsin(x) is 2pi^2