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

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

Popular >

integral from 0 to pi of 2pix(sin(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}

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

\int_{0}^{\frac{3 π}{2}} (∣ sin (x) ∣) d x

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

\int_{1}^{x^{3}} \frac{1}{1 + ln ( t )} d t

\int_{- 3}^{3} 3^{2} - x^{2} d x

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