What is the integral from 0 to pi of sin(x)cos(n)x ?

The integral from 0 to pi of sin(x)cos(n)x is cos(n)pi

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integral from 0 to pi of sin(x)cos(n)x

\int_{0}^{π} sin (x) cos (n) x d x

cos (n) π

Solution steps

\int_{0}^{π} sin (x) cos (n) x d x

Take the constant out:

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

= cos (n) \cdot \int_{0}^{π} sin (x) x d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Compute the boundaries:

π

= cos (n) π

\int_{0}^{40} 0.3 x d x

\int_{0}^{π} 3 x^{2} cos (\frac{x}{2}) d x

\int_{0}^{π} (9 sin (x)) d x

\int_{0}^{1} (4 + r)^{3} d r

\int_{0}^{\frac{1}{2}} \frac{x ^{2}}{2 x + 1} d x

What is the integral from 0 to pi of sin(x)cos(n)x ?
The integral from 0 to pi of sin(x)cos(n)x is cos(n)pi