What is the solution of ∫sin³x.dx Should i put t=cosx³ and then solve it
What is the solution of ∫sin³x.dx
Should i put t=cosx³ and then solve it
ARYAN YADAV , 6 Years ago
Grade 12
Trigonometry> What is the solution of ∫sin³x.dx Shoul...
1 Answers
Arun
Last Activity: 6 Years ago
Assuming you don't want to use the reduction formula . . . . .
∫ sin³x dx = ∫sinx(1 – cos²x) dx
u = cosx
du/dx = - sinx
- du = sinx dx
- ∫ (1 – u²) du =
- ∫du + ∫u² du =
-u + (u³/3) + C =
-cosx + (cos³x)/3 + C =
C – cosx + (cos³x)/3 =
and this can be simplified by factoring cosx and using identities
C + [ (cos(3x) – 9cos(x)) / 12 ]
∫ sin³x dx = ∫sinx(1 – cos²x) dx
u = cosx
du/dx = - sinx
- du = sinx dx
- ∫ (1 – u²) du =
- ∫du + ∫u² du =
-u + (u³/3) + C =
-cosx + (cos³x)/3 + C =
C – cosx + (cos³x)/3 =
and this can be simplified by factoring cosx and using identities
C + [ (cos(3x) – 9cos(x)) / 12 ]
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