What is the integral from-2 to 9 of-x*cos(x) ?

The integral from-2 to 9 of-x*cos(x) is -9sin(9)-cos(9)+2sin(2)+cos(2)

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integral from-2 to 9 of-x*cos(x)

\int_{- 2}^{9} - x \cdot cos (x) d x

- 9 sin (9) - cos (9) + 2 sin (2) + cos (2)

Decimal

- 1.39548 \dots

Solution steps

\int_{- 2}^{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_{- 2}^{9} x cos (x) d x

Apply Integration By Parts

: [x sin (x) - \int sin (x) d x]_{- 2}^{9}

= - [x sin (x) - \int sin (x) d x]_{- 2}^{9}

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

= - [x sin (x) - (- cos (x))]_{- 2}^{9}

Simplify

= - [x sin (x) + cos (x)]_{- 2}^{9}

Compute the boundaries:

9 sin (9) + cos (9) - 2 sin (2) - cos (2)

= - (9 sin (9) + cos (9) - 2 sin (2) - cos (2))

Simplify

= - 9 sin (9) - cos (9) + 2 sin (2) + cos (2)

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\int_{0}^{4} \frac{x ^{2}}{x ^{3} + 6} d x

\int_{0}^{3} (\frac{1}{2} x^{3} - 3 x) d x

\int_{1}^{4} (8 x^{2} - 6 x + 4) d x

What is the integral from-2 to 9 of-x*cos(x) ?
The integral from-2 to 9 of-x*cos(x) is -9sin(9)-cos(9)+2sin(2)+cos(2)