What is the integral from 0 to pi/4 of tsin(t) ?

The integral from 0 to pi/4 of tsin(t) is 1/(sqrt(2))-pi/(4sqrt(2))

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integral from 0 to pi/4 of tsin(t)

\int_{0}^{\frac{π}{4}} t sin (t) d t

\frac{1}{2} - \frac{π}{4 2}

Decimal

0.15174 \dots

Solution steps

\int_{0}^{\frac{π}{4}} t sin (t) d t

Apply Integration By Parts

: [- t cos (t) - \int - cos (t) d t]_{0}^{\frac{π}{4}}

= [- t cos (t) - \int - cos (t) d t]_{0}^{\frac{π}{4}}

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

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

Simplify

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

Compute the boundaries:

\frac{1}{2} - \frac{π}{4 2}

= \frac{1}{2} - \frac{π}{4 2}

\int_{0}^{2} x^{2} (\frac{3}{4} x (2 - x)) d x

\int_{0}^{1} (1 - x) x^{n} d x

\int_{3}^{5} x^{3} x^{2} - 4 d x

\int_{1}^{5} 6 x d x

\int_{0}^{2} x sin (n x) d x

What is the integral from 0 to pi/4 of tsin(t) ?
The integral from 0 to pi/4 of tsin(t) is 1/(sqrt(2))-pi/(4sqrt(2))