I have no clue how to do this. Please help. Thank you!
2007-10-30 02:10:19 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
y = Sin(x^3)
=> dy/dx = cos (x^3) * 3x^2
2007-10-30 02:20:07 · answer #1 · answered by harry m 6 · 0⤊ 4⤋
Using Mathematica, the solution involves the gamma function, i.e. this problem is not commonly solved by hand. Or, if it is a typo, would you have meant sin³x? i.e. (sinx)³. If so, use the identity
sin³x = (1/4)(3sinx - sin3x)
and integrate each term.
* a more common form of this identity is
sin(3x) = 3sinx - 4sin³x
2007-10-30 09:27:36 · answer #2 · answered by W 3 · 0⤊ 0⤋
You have no clue how to do this because
the integral is not elementary! It's solution
involves the incomplete gamma function.
In general, the integral of sin[x^a] (a .ne. 1) is
not elementary.
2007-10-30 09:23:57 · answer #3 · answered by steiner1745 7 · 1⤊ 0⤋