What is the integral from pi/2 to sqrt(x of)sin(9t) ?

The integral from pi/2 to sqrt(x of)sin(9t) is -1/9 cos(9sqrt(x))

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integral from pi/2 to sqrt(x of)sin(9t)

\int_{\frac{π}{2}}^{x} sin (9 t) d t

- \frac{1}{9} cos (9 x)

Solution steps

\int_{\frac{π}{2}}^{x} sin (9 t) d t

Apply u-substitution

: \int_{\frac{9 π}{2}}^{9 x} sin (u) \frac{1}{9} d u

= \int_{\frac{9 π}{2}}^{9 x} sin (u) \frac{1}{9} d u

Take the constant out:

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

= \frac{1}{9} \cdot \int_{\frac{9 π}{2}}^{9 x} sin (u) d u

Use the common integral:

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

= \frac{1}{9} [- cos (u)]_{\frac{9 π}{2}}^{9 x}

Compute the boundaries:

- cos (9 x)

= \frac{1}{9} (- cos (9 x))

Simplify

= - \frac{1}{9} cos (9 x)

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What is the integral from pi/2 to sqrt(x of)sin(9t) ?
The integral from pi/2 to sqrt(x of)sin(9t) is -1/9 cos(9sqrt(x))