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

The integral from 0 to sqrt(pi of)xsin(x^2) is 1

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

\int_{0}^{π} x sin (x^{2}) d x

1

Solution steps

\int_{0}^{π} x sin (x^{2}) d x

Apply u-substitution

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

= \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

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

Use the common integral:

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

= \frac{1}{2} [- cos (u)]_{0}^{π}

Compute the boundaries:

2

= \frac{1}{2} \cdot 2

Simplify

= 1

x \to - 5 lim (\frac{x ^{2} - 5}{x + 5})

x = 2 y^{2}, x = 2

y^{^{''}} - 2 y^{^{'}} - 15 y = e^{(3 x)} cos (2 x)

\frac{d}{d x} (x^{2} sin (x^{3}))

\frac{d}{d x} (\frac{1}{xx})

What is the integral from 0 to sqrt(pi of)xsin(x^2) ?
The integral from 0 to sqrt(pi of)xsin(x^2) is 1