What is the integral from 0 to pi of 7xsin(x) ?

The integral from 0 to pi of 7xsin(x) is 7pi

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integral from 0 to pi of 7xsin(x)

\int_{0}^{π} 7 x sin (x) d x

7 π

Decimal Notation

21.99114 \dots

Solution steps

\int_{0}^{π} 7 x sin (x) d x

Take the constant out:

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

= 7 \cdot \int_{0}^{π} x sin (x) d x

Apply Integration By Parts

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

= 7 [- x cos (x) - \int - cos (x) d x]_{0}^{π}

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

= 7 [- x cos (x) - (- sin (x))]_{0}^{π}

Simplify

= 7 [- x cos (x) + sin (x)]_{0}^{π}

Compute the boundaries:

π

= 7 π

\int_{7}^{- 5} g (x) d x

\int_{0}^{8} 2 x e^{- 0.2 x} d x

\int_{1}^{3} 3 x 2 x + 3 d x

\int_{0}^{7} \frac{1}{( x - 3 ) ^{2}} d x

\int_{1}^{2} x \frac{3}{7} x^{2} d x

What is the integral from 0 to pi of 7xsin(x) ?
The integral from 0 to pi of 7xsin(x) is 7pi