Solving Riemann-Stieltjes integral:$int_{- pi/4}^{pi/4} f(x)dg(x)$
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I'm having trouble solving this Riemann-Stieltjes integral: $$int_{- pi/4}^{pi/4} f(x)dg(x),$$ where $$f(x):= begin{cases} frac{sin^4x}{cos^2x}{} &text{if }xge0, \{}\ frac1{cos^3x} &text{if }x<0,end{cases}$$ and $$g(x)=begin{cases} phantom{-} 1+sin(x) &text{if }-pi/4 <x<pi/4, \ -1 &text{otherwise}.end{cases}$$ I believe the only jump discontinuities are at $-pi/4$ and $pi/4$ . Which $g=-1$ at both of those points. I'm struggling with the rest. What formula should I be using to compute the integral and what should my answer look like? Thanks for any help!
real-analysis calculus integration trigonometry stieltjes-integral
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