evaluate:
∫1/x dx; n=8 on (1,2)

Question

across · Answer

$$\int\frac{1}{x}dx.$$What's confusing about this integral?

anonymous · Answer

if you integrate it, you get x^0... so it's lnx but then i'm lost on finding the area

across · Answer

That's correct.$$\int\frac{1}{x}dx=\ln|x|.$$Now, what does that n stand for?

anonymous · Answer

the number of intervals?

across · Answer

I suppose (1, 2) is the range in which these intervals are partitioned?

anonymous · Answer

yes

across · Answer

If that's the case, then to solve this problem, you have to make use of the limit definition of an integral.

anonymous · Answer

okay... how would i write that out?

across · Answer

$$\int_{a}^{b}f(x)=\lim_{n\to\infty}\sum_{i=1}^{n}f(c_{i})\Delta x_{i}.$$

anonymous · Answer

is there a way to do it without the greek E? we are on chapter 7.3 and haven't learned that... but we do know limits

jamesj · Answer

So for your problem you have eight partitions?

jamesj · Answer

Assuming so, then let x_i = 1 + i/8, i =1, 2, 3, ..., 8.

Then you want an approximation of the Riemann integral such as

1/8 [ f(x_1) + f(x_2) + ... + f(x_8) ]

where f(x) = 1/x