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

The integral from 0 to x of tsin(t) is sin(x)-xcos(x)

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integral from 0 to x of tsin(t)

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

sin (x) - x cos (x)

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Compute the boundaries:

sin (x) - x cos (x)

= sin (x) - x cos (x)

\int_{1}^{4} u d u

\int_{0}^{1} x^{4} (1 + 2 x^{5})^{5} d x

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

\int_{0}^{x} f (t) sin (x - t) d t

\int_{- 1}^{8} 1 + x d x

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