Question

Check my work?!

Answer 1

So heres the question
\[\lim_{n \rightarrow \infty} \sum_{i=1}^{n} x i^9 - \frac{ 3\tan(x i }{ x i } Deltax\]

Answer 2

Heres how i solved

Answer 3

\[\int\limits_{0}^{\pi/3} \frac{ x^9-3\tan(x)dx }{ x }\]

Answer 4

My question is, is the "i" always ignored, or am i ignoring the i in this case because it is equal to 1

Answer 5

(Question asked express the limit as a definite intergral)

Answer 6

I will focus only on your personal question here. We are not "ignoring" the counter, " i ". Note that we count from 1 to n; this produces n terms that have to be combined (summed up). In the very end we take the limit of that result as n approaches infinity. As you're probably aware, this is a Riemann Sums problem.

Answer 7

We don't actually sum up hundreds and millions of individual terms (representing thin vertical slices of area), but rather separate the integrand so that you have, instead, sums that look like \[\sum_{i=1}^{n}1=n;~\sum_{i=1}^{n}i=\frac{ n(n+1) }{ 2 };~\sum_{i=1}^{n}i^2=\frac{ n(n+1)(2n+1) }{6 }\] and so on.

Answer 8

Please forgive me, but i need to get off the 'Net now. Good luck! By all means come back if you have further Riemann Sums problems to discuss.

Answer 9

Was my solved answer incorrect? but thank you!:)

Answer 10

One last thing: I'm not as familiar with the use of this method where trig functions are involved. I'd suggest that you choose another problem involving a polynomial that is at just the right level that you can solve it; work your way up to harder problems, and then, finally, tackle this one involving a trig function.

Answer 11

Is it possible that by

\[\lim_{n \rightarrow \infty} \sum_{i=1}^{n} x i^9\Delta x\]

Answer 12

you actually meant this? \[\lim_{n \rightarrow \infty} \sum_{i=1}^{n} x _{i} ^{9} \Delta x\]???