Question

Question #0ae43

Answer 1

∫ t sin 9t dt = `1/81 (sin(9t) - 9t * cos(9t))`
Use integration by parts to solve.

Explanation:

Using integration by parts:

∫ t sin 9t dt = `t*int sin(9t) dt - int(int sin(9t) dt) dt`

∫ t sin 9t dt = `t*(-cos(9t)/9) - int(-cos(9t)/9) dt`

∫ t sin 9t dt = `-tcos(9t)/9 + sin(9t)/81`

∫ t sin 9t dt = `1/81 (sin(9t) - 9t * cos(9t))`

Please ask if you need more help using integration by parts.

Rory.