What is the integral from-3 to 9 of-xcos(x) ?

The integral from-3 to 9 of-xcos(x) is -9sin(9)-cos(9)+3sin(3)+cos(3)

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integral from-3 to 9 of-xcos(x)

\int_{- 3}^{9} - x cos (x) d x

- 9 sin (9) - cos (9) + 3 sin (3) + cos (3)

Decimal

- 3.36456 \dots

Solution steps

\int_{- 3}^{9} - x cos (x) d x

Take the constant out:

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

= - \int_{- 3}^{9} x cos (x) d x

Apply Integration By Parts

: [x sin (x) - \int sin (x) d x]_{- 3}^{9}

= - [x sin (x) - \int sin (x) d x]_{- 3}^{9}

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

= - [x sin (x) - (- cos (x))]_{- 3}^{9}

Simplify

= - [x sin (x) + cos (x)]_{- 3}^{9}

Compute the boundaries:

9 sin (9) + cos (9) - 3 sin (3) - cos (3)

= - (9 sin (9) + cos (9) - 3 sin (3) - cos (3))

Simplify

= - 9 sin (9) - cos (9) + 3 sin (3) + cos (3)

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What is the integral from-3 to 9 of-xcos(x) ?
The integral from-3 to 9 of-xcos(x) is -9sin(9)-cos(9)+3sin(3)+cos(3)