What is the integral from 0 to sqrt(pi of)3xsin(x^2) ?

The integral from 0 to sqrt(pi of)3xsin(x^2) is 3

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integral from 0 to sqrt(pi of)3xsin(x^2)

\int_{0}^{π} 3 x sin (x^{2}) d x

3

Solution steps

\int_{0}^{π} 3 x sin (x^{2}) d x

Take the constant out:

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

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

Apply u-substitution

: \int_{0}^{π} \frac{sin ( u )}{2} d u

= 3 \cdot \int_{0}^{π} \frac{sin ( u )}{2} d u

Take the constant out:

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

= 3 \cdot \frac{1}{2} \cdot \int_{0}^{π} sin (u) d u

Use the common integral:

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

= 3 \cdot \frac{1}{2} [- cos (u)]_{0}^{π}

Simplify

3 \cdot \frac{1}{2} [- cos (u)]_{0}^{π} : \frac{3}{2} [- cos (u)]_{0}^{π}

= \frac{3}{2} [- cos (u)]_{0}^{π}

Compute the boundaries:

2

= \frac{3}{2} \cdot 2

Simplify

= 3

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What is the integral from 0 to sqrt(pi of)3xsin(x^2) ?
The integral from 0 to sqrt(pi of)3xsin(x^2) is 3