What is the integral from 0 to 2pi of tsin(2t) ?

The integral from 0 to 2pi of tsin(2t) is -pi

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integral from 0 to 2pi of tsin(2t)

\int_{0}^{2 π} t sin (2 t) d t

- π

Decimal

- 3.14159 \dots

Solution steps

\int_{0}^{2 π} t sin (2 t) d t

Apply Integration By Parts

: [\frac{1}{2} (- t cos (2 t) - 2 \cdot \int - \frac{1}{2} cos (2 t) d t)]_{0}^{2 π}

= [\frac{1}{2} (- t cos (2 t) - 2 \cdot \int - \frac{1}{2} cos (2 t) d t)]_{0}^{2 π}

\int - \frac{1}{2} cos (2 t) d t = - \frac{1}{4} sin (2 t)

= [\frac{1}{2} (- t cos (2 t) - 2 (- \frac{1}{4} sin (2 t)))]_{0}^{2 π}

Simplify

[\frac{1}{2} (- t cos (2 t) - 2 (- \frac{1}{4} sin (2 t)))]_{0}^{2 π} : [\frac{1}{2} (- t cos (2 t) + \frac{1}{2} sin (2 t))]_{0}^{2 π}

= [\frac{1}{2} (- t cos (2 t) + \frac{1}{2} sin (2 t))]_{0}^{2 π}

Compute the boundaries:

- π

= - π

f (x) = (2 x - 6)^{4} (x^{2} + x + 1)^{5}

\frac{d}{d x} (\frac{( x - 1 )}{x ^{2}})

\frac{d}{d x} (2 x^{2} - x^{3})

\int (x^{2} - 5)^{2} 0.2 x d x

\int_{6}^{7} \frac{x}{x - 6} d x

What is the integral from 0 to 2pi of tsin(2t) ?
The integral from 0 to 2pi of tsin(2t) is -pi