- #1
Chadlee88
- 41
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Could someone please help me integrate (sin x)^3. Can i use any simpler method asides from integration by parts.??
The formula for integrating (sin x)^3 is:
∫ (sin x)^3 dx = ∫ sin^2 x * sin x dx
Yes, (sin x)^3 can be simplified without using integration by parts by using the trigonometric identity sin^2 x = (1 - cos 2x)/2.
The general approach for simplifying (sin x)^3 without integration by parts is to use the trigonometric identity sin^2 x = (1 - cos 2x)/2 to rewrite the integral as:
∫ (sin x)^3 dx = ∫ (1 - cos 2x)/2 * sin x dx
After simplifying (sin x)^3, the resulting integral can be solved by applying the power rule, integration by substitution, or integration by parts.
The final solution for integrating (sin x)^3 without using integration by parts is:
∫ (sin x)^3 dx = -cos x - (1/4) * cos 3x + C