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The paradox is that the limit sign panetrated through the integral sign and left an incomplete infinity 1/x, and continue to influence following steps.
After simplification they are both ln2 (log2) !!!
It took my software 2 minutes to compute n=7 case and 7 minutes to compute n=18 case. Although it didn't return ln2, the numerical approximation are both 0.693147 ! ! !
I admit my method is wrong, because the trapezoid fails to approximate even
So is the answer ln2 instead? It depends on whether (sint)n/tn+1 can be treated as 1/t.
is anyone able to do the integration and ignore the limit, i.e. just add a constant in the end.
Franklin wrote: but the answer is likely zero the the area under the curve from 0 to 0, unless n is way bigger than m- Right
the question is like what ganesh wrote, this is the question i meant to post but i couldn't type it probably.x shouldn't be same as t, should be independent of t. i think the question want me to do the integration, and then put 2x and x in as the answer, and then limit x->0.
There's no x in the equation, so what does it mean? Maybe x should be t and then it may depend if the sine is in radians or degrees, but the answer is likely zero the the area under the curve from 0 to 0, unless n is way bigger than m. Forget about n bigger than m, that part might be wrong. If x is t, then nearly 0 to the power of number 1 or above makes the number get even smaller because a root would make near zero approach a tiny ways toward one (and this is a power, not a root.)
doraeyee_u_v's question is
evaluate the limit