The given integral is I . n = ∫ sin n ⁡ ( x ) d x " id="MathJax-Element-52-Frame" role="presentation" style="position: relative;" tabindex="0">I . n = ∫ sin n ⁡ ( x ) d x " id="MathJax-Element-98-Frame" role="presentation" style="position: relative;" tabindex="0">
. If \( I.n = -\frac{1}{n} \sin^{n-1}(x) \cos(x) + \frac{n-1}{n} I.{n-2} \) , then what is \(\int \sin^4(x) \, dx \) ?
1
\(-\frac{1}{4} \sin^3(x) \cos(x) + \frac{3}{4} \int \sin^2(x) \, dx \)
2
\( -\frac{1}{4} \sin^3(x) \cos(x) + \frac{3x}{8} - \frac{3}{16} \sin(2x) \)
3
\(-\frac{1}{4} \sin^3(x) \cos(x) + \frac{3}{4} x \)
4
None of the above