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

The integral from 0 to t of tsin(t) is -tcos(t)+sin(t)

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integral from 0 to t of tsin(t)

\int_{0}^{t} t sin (t) d t

- t cos (t) + sin (t)

Solution steps

\int_{0}^{t} t sin (t) d t

Apply Integration By Parts

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

= [- t cos (t) - \int - cos (t) d t]_{0}^{t}

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

= [- t cos (t) - (- sin (t))]_{0}^{t}

Simplify

= [- t cos (t) + sin (t)]_{0}^{t}

Compute the boundaries:

- t cos (t) + sin (t)

= - t cos (t) + sin (t)

\int_{0}^{4} x^{2} + 2 d x

\int_{0}^{2} x 1 - x^{2} d x

\int_{0}^{θ} x (\frac{2 x}{θ ^{2}}) d x

\int_{- 1}^{1} - x^{2} + 2 d x

\int_{- 4}^{2} \frac{2 x}{3 x ^{2} + 10} d x

What is the integral from 0 to t of tsin(t) ?
The integral from 0 to t of tsin(t) is -tcos(t)+sin(t)