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

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

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

\int_{0}^{π} x \cdot 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

\int_{3}^{4} \frac{2}{25 - x ^{2}} d x

\int_{0}^{x} (e^{t^{2}} - 1) d t

\int_{0}^{4} 3 t - 7 d t

\int_{0}^{1} 3 x - 3 x^{2} d x

\int_{0}^{4} 2 x e^{x^{2}} d x

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