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

The integral from 0 to sqrt(x of)xcos(x^2) is 1/2 sin(x)

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

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

\frac{1}{2} sin (x)

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

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

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

Compute the boundaries:

sin (x)

= \frac{1}{2} sin (x)

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

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

\int_{1}^{x} \frac{e ^{t}}{t} d t

\int_{0}^{1} (1 - x)^{5} d x

\int_{0}^{1} (1 - y)^{2} d y

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