Math Is Fun Forum

You left the dx. This is where you got wrong because now if you are integrating with u/v, you should also change the dx to anything like du or dv. Can you please tell me the complete question?

Let, u = g(x)

Differentiate both sides with respect to x:

Now sub. back in the integral:

This is the simplest to what I know. If you give me the original equation, I might help you solving it.

Ok that's strange and I had never seen such thing before

Hey dude, I calculated 100s of values and the final approximate answer was 0 as shown in the figure. You can see the complete execution at https://ktesla.infy.uk/math.html But only open if you are on a PC as this has various nested loops that might hang your computer a bit (3 GB RAM)

Thanks Bob!

I'll definitely love that.

Tomorrow I have exam of Optional Mathematics and I'll ask my teacher about the question. Maybe he can help.

Ok now I don't seek any way to prove the equation. I tried dozens of methods and the only thing I can say is -- This cant be proved using pure algebra. I may be wrong but I'll be still good if we get any solution.

I am in class 10 and I've started learning calculus (class 11) and after some time, when I'll find myself ready, I'll try learning Taylor Series and the Reimann zeta function. once I had a question something like

. I couldn't solve this and when I asked someone about it, they replied that this was a non elementary function an is written as Ei(x). That time I first saw Gamma and Zeta function.

Not actually because I'm just few years ahead of you and still I don't know much about Calculus. The only thing I know is that this can be proved using Taylor Series which is really complex. ?

This can be solved using calculus but to keep things easier, I just have a way: calculate everything from both LHS and RHS.
LHS = 1 + 1/16 + 1/81 + 1/256...... (notice that's decreasing rapidly when we increase n. So few numbers might give correct result. I'll use only 8 terms:)
       = 1 + 0.0625 + 0.0123 + 0.00390625 + 0.0016 + 0.0007716049 + 0.000416493 + 0.0002441406
       = 1.0815
RHS = 1.082

They are found to be equal up to 3 decimals and if you want more accuracy use more digits.

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Hi guys!

In Nepal, we are mainly taught 3 ways of solving quadratic equations: product sum method, completing square method and the formula method. You can read the whole chapter here: https://lms.neemaacademy.com/course/2095/School-Mathematics-Grade-10/component/ynPP0L

In the product sum method, which only works for integers, we do the steps:

For any equation like:

, we do:
- Multiply a with c to make ac
- Check whether it's sum or difference, if c > 0, it's sum else it's difference
- Find two numbers whose sum or difference is b and product is ac
- Once you have the numbers, keep them instead of b in the equation.

For example:

Here, ac = 6*(-10) = -60; use difference
The numbers whose product is 60 and difference is 11 are: 15 and 4.

Hence (2x+5) and (3x-2) are the solutions.

Hi,