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

The integral from 0 to t of xsin(x) is sin(t)-tcos(t)

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integral from 0 to t of xsin(x)

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

sin (t) - t cos (t)

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Compute the boundaries:

sin (t) - t cos (t)

= sin (t) - t cos (t)

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\int_{\frac{π}{3}}^{x} cot^{2} (t) d t

\int_{- 1}^{2} (3 u - 5) (u + 2) d u

\int_{- 2}^{5} ∣ x ∣ d x

\int_{0}^{1} x^{6} e^{- x^{7}} d x

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