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

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

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integral from 0 to pi of sin(x)x

\int_{0}^{π} sin (x) x d x

π

Decimal

3.14159 \dots

Solution steps

\int_{0}^{π} sin (x) x d x

Apply Integration By Parts

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

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

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

= [- x cos (x) - (- sin (x))]_{0}^{π}

Simplify

= [- x cos (x) + sin (x)]_{0}^{π}

Compute the boundaries:

π

= π

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\int_{- \frac{π}{6}}^{0} tan (x) d x

\int_{4}^{7} 3 + 2 ln (x + 5) d x

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

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