MIT Integration 2023 , Q1
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- Опубліковано 30 січ 2023
- MIT Integration Bee Qualifying Exam -2023 : Q. 1
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#integrationtechniques #integrals #mathcompetition #mitintegrationbee #integration #mathstricks
another way,
substitute logx=t
so x=e^t,
and dx=e^t * dt,
so integral (e^t)^(1/t) * e^t * dt,
which is integral e * e^t dt
on solving is e*e^t + c
on substituting e^t as x
final answer is e*x + c.
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X^(1/log_a_x) can be written as x^(log_x_a)
Then we can continue easily from this step
Thank you for your comment!
You are correct that X^(1/log_a_x) can be written as x^(log_x_a) using the change-of-base formula for logarithms. This simplification can make it easier to work with the expression.
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We , when preparing for jee , do such problems for boosting confidence.
😅
That's great to hear! Practicing problems is definitely a good way to boost confidence and reinforce your understanding. Keep up the hard work and stay focused. Best of luck with your JEE preparation!
Um, the correct answer should be 10x+C. The log(x) is referring to the common log, which is log base 10. Unless you mean ln(x), then it's log base e. Otherwise, if you mean the integral of x^(1/ln(x))dx, then it's ex+C.
Hi Justin Lee,
"Thank you for taking the time to provide additional information! I appreciate your input and will keep it in mind for future videos. Thank you for helping to clarify this point for our viewers.
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Refer the integration bee general rules set. They cleary mention all logs are to the base e.
@@PXO005 I don't think so. In math, chemistry, and physics, we always write ln(x), which is referring to log base e. If you say log(x) without a base written, then it's always going to be log base 10 or the common log. I have never heard of something that log(x) is the same as ln(x). That is unclear and is very confused.
Thank you for your comment and for sharing this information! .In this particular video, I was using the natural logarithm, which is commonly denoted by 'ln(x)' and is to the base e. However, it's always helpful to review different sources and perspectives, so thank you again for sharing this resource.
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@@justabunga1 yes, I understand what you mean.. But bro you can't argue with the rules of the competition.. They set the rule that log(x) means base e
This is actually not hard, the only thing is that it looks scary.
Thank you for sharing your thoughts!
You're absolutely right - sometimes things may seem intimidating or scary at first, but with practice and perseverance, they can become much easier. Keep up the great work!
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@@MathsTuts4U absolutely 👍
Thanks a lot
Sir, can we do it by this:
1)multiplying and dividing by x
2)putting logx = t and then applying the known formula
pls reply.
Hello Naman!
Thank you for your comment and suggestion. You're on the right track.
Multiplying and dividing by x and using logarithmic substitution are both common methods for solving integrals.
Using logarithmic substitution, as you suggest, is particularly useful for integrals involving exponential functions.
It's great to see you're thinking critically about the problem and finding creative ways to approach it.
Keep up the good work !
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e^log x = x
therefore (e^log x)^1/log x = e = x^1/log x
ok
As Jee Aspirant , like these questions are too easy 🗿🗿
ok
Shouldn't the answer be e *x not e^x.integrating e^1dx in last step e is an constant and integration of dx is x. Hence e *x +c
Thank you for your comment! I appreciate your input. However, when integrating the function e^x, we don't treat e as a constant like we do with other coefficients. Instead, the integral of e^x is indeed e^x itself.
To clarify, when we integrate e^x with respect to x, the result is e^x, not e times x. This is because the derivative of e^x is e^x itself. The exponential function e^x has a special property where its derivative and integral are the same.
So, when integrating e^x, the correct answer is e^x + C, where C represents the constant of integration. The integral of dx is indeed x, but the coefficient in front of x remains as e.
I hope this clears up any confusion. If you have any more questions, feel free to ask!
@@MathsTuts4Uwe were not integrating e^x ?
The final result was integral(e^1. dx ) which is e.integral(dx) whose answer is e.x not e^x?? (Using "." instead of "*" to clear confusion)
e is a constant after all isn't it. You yourself wrote ex+c(which is correct) but spoke out "e raise to x" which is clearly wrong.
i learned integration 2 days Ago And When This Came I was Like Eh This Was MIT question 😂😂 So easy
Proceeds to get fked Up
Thanks
Shouldn’t it be e^x? The log and 1/log gets cancel but the x is still left there
Hi Samuel,
When we cancel out the terms of log(x) and 1/log(x), we are left with only the constant value of 'e'. It's important to note that the logarithmic function cannot stand alone, and it should always be associated with a variable, such as 'x'
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@@MathsTuts4U He is confused since you write the multiplication sign as an "x". It could be missunderstood as "1/log(x)*x*log(x)" which he did.
Shouldn't it be 10^log...?
Hi Mark,
"Thank you for pointing that out! You're correct, it should indeed be 10^log instead of log^10. we can solve in that way also.I appreciate your attention to detail and for bringing this to my attention. I hope my content has been helpful to you.
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ex answer
Thanks
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Thanks