(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that the integral of sin(t)/t+1 dt from 0 to x is greater than 0 for all x > 0

2. Relevant equations

If f is bounded on [a,b], then f is integrable on [a,b] iff for every epsilon > 0 there exists a partition P of [a,b] s.t. U(f,P) - L(f,P) < epsilon.

3. The attempt at a solution

When you graph sin(t)/t+1 for t>=0, you get a sinusoidal graph with humps that get smaller and smaller, close to the horizontal axis. So using the definition of the integral as the area under the curve, it would make sense that integral of sin(t)/t+1 dt from x to 0 is greater than 0 along the positive x-axis, since the curve becomes almost insignificant as x>0, so the only area that "counts" is the first hump.

I'm stuck on how to do a formal proof, though. Any help would be much appreciated. Moreover, the graph is not bounded. Thanks!

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# Homework Help: Proof for integral of sin(t)/t+1 dt from x to 0

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