What is the integral from 1 to 7 of-tsin(t) ?

The integral from 1 to 7 of-tsin(t) is 7cos(7)-sin(7)-cos(1)+sin(1)

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integral from 1 to 7 of-tsin(t)

\int_{1}^{7} - t sin (t) d t

7 cos (7) - sin (7) - cos (1) + sin (1)

Decimal

4.92149 \dots

Solution steps

\int_{1}^{7} - t sin (t) d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int_{1}^{7} t sin (t) d t

Apply Integration By Parts

: [- t cos (t) - \int - cos (t) d t]_{1}^{7}

= - [- t cos (t) - \int - cos (t) d t]_{1}^{7}

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

= - [- t cos (t) - (- sin (t))]_{1}^{7}

Simplify

= - [- t cos (t) + sin (t)]_{1}^{7}

Compute the boundaries:

- 7 cos (7) + sin (7) + cos (1) - sin (1)

= - (- 7 cos (7) + sin (7) + cos (1) - sin (1))

Simplify

= 7 cos (7) - sin (7) - cos (1) + sin (1)

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What is the integral from 1 to 7 of-tsin(t) ?
The integral from 1 to 7 of-tsin(t) is 7cos(7)-sin(7)-cos(1)+sin(1)