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

The integral from 0 to sqrt(x of)xsin(x^2) is 1/2 (-cos(x)+1)

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

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

\frac{1}{2} (- cos (x) + 1)

Solution steps

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

Apply u-substitution

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

= \int_{0}^{x} \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}^{x} sin (u) d u

Use the common integral:

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

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

Compute the boundaries:

- cos (x) + 1

= \frac{1}{2} (- cos (x) + 1)

\int_{0}^{1} \frac{6}{5} (x + y^{2}) d y

\int_{4}^{5} 3 x x - 4 d x

\int_{1}^{4} (2 x + 3) d x

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

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

What is the integral from 0 to sqrt(x of)xsin(x^2) ?
The integral from 0 to sqrt(x of)xsin(x^2) is 1/2 (-cos(x)+1)