What is the integral from pi/2 to sqrt(x of)sin(15x) ?

The integral from pi/2 to sqrt(x of)sin(15x) is -1/15 cos(15sqrt(x))

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integral from pi/2 to sqrt(x of)sin(15x)

\int_{\frac{π}{2}}^{x} sin (15 x) d x

- \frac{1}{15} cos (15 x)

Solution steps

\int_{\frac{π}{2}}^{x} sin (15 x) d x

Apply u-substitution

: \int_{\frac{15 π}{2}}^{15 x} sin (u) \frac{1}{15} d u

= \int_{\frac{15 π}{2}}^{15 x} sin (u) \frac{1}{15} d u

Take the constant out:

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

= \frac{1}{15} \cdot \int_{\frac{15 π}{2}}^{15 x} sin (u) d u

Use the common integral:

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

= \frac{1}{15} [- cos (u)]_{\frac{15 π}{2}}^{15 x}

Compute the boundaries:

- cos (15 x)

= \frac{1}{15} (- cos (15 x))

Simplify

= - \frac{1}{15} cos (15 x)

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What is the integral from pi/2 to sqrt(x of)sin(15x) ?
The integral from pi/2 to sqrt(x of)sin(15x) is -1/15 cos(15sqrt(x))