Is there something wrong?
After sub x=0.1 into the final answer, I found that the value is not same. Thank you!
#1015578016606343218
#integration question
balmy root
spice solarBOT
Is there something wrong?
After sub x=0.1 into the final answer, I found that th...
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gray bridge
Is there something wrong?
After sub x=0.1 into the final answer, I found that th...
Show your work between lines 1 and 2 on the second page.
balmy root
Now explain the substitution please?
That’s universal substitution, which can be used for k+sinx that is in the denominator
gray bridge
Well, that's the most complicated looking step, so I'd suspect that's where the mistake is.
If there is one.
Which there might not be, your method of checking is flawed.
balmy root
Which there might not be, your method of checking is flawed.
What method of checking is better in this case?
gray bridge
What method of checking is better in this case?
Well, first, let's address the flaw in this method of checking. You notice, of course, the + c.
balmy root
Well, first, let's address the flaw in this method of checking. You notice, of c...
Ok, I found that difference of answers of two method is 1, maybe it’s due to +C
gray bridge
Could be.
If they do only differ by a constant, then they are in fact both antiderivatives of the integrand.
And what's the definition of an antiderivative?
balmy root
After differentiating the function that is integrated, that would be equal to the original function
balmy root
If they do only differ by a constant, then they are in fact both antiderivatives...
How to check the answer in this case?
gray bridge
After differentiating the function that is integrated, that would be equal to th...
No. You seem to understand but you didn't say it right. A function f is an antiderivative of a function g if and only if g is the derivative of f.
balmy root
No. You seem to understand but you didn't say it right. A function f is an antid...
ok, I see
gray bridge
Therefore, to prove that a function f is an antiderivative of a function g, what must you do?
balmy root
is the answer sec(pi/4 - x/2) -x + c ?
should be no
balmy root
the argument of the trig function
argument is pi/4-x/2 ?
woven nymph
argument is pi/4-x/2 ?
and the answer is not sec(pi/4 - x/2) - x +c?
can u send me the pic of answer rq?
gray bridge
Differentiating f ?
Exactly, you must prove that g is the derivative of f.
balmy root
Exactly, you must prove that g is the derivative of f.
I’ve differentiating the answer, that is same as the function in the question
gray bridge
I’ve differentiating the answer, that is same as the function in the question
Which answer? Remember you got two, and you want to know whether they're both correct.
balmy root
Both of two are correct
But there’s a question, if we’re doing definite integration, this will also lead to two different answers
woven nymph
mb it was -2tan(pi/4-x/2) -x+c
balmy root
mb it was -2tan(pi/4-x/2) -x+c
After integration? Seems not correct
woven nymph
After integration? Seems not correct
how do u know ? did u differnetiate it?
gray bridge
But there’s a question, if we’re doing definite integration, this will also lead...
Will it?
woven nymph
mb it was -2tan(pi/4-x/2) -x+c
after u differntiateit
balmy root
how do u know ? did u differnetiate it?
Yes, just use differentiation calculator and then sub x=0.1 / 0.2 to check
woven nymph
u get sec^2(pi/4-x/2) -1
woven nymph
Yes, just use differentiation calculator and then sub x=0.1 / 0.2 to check
w-what
woven nymph
u get sec^2(pi/4-x/2) -1
this beceoms tan^2(pi/4-x/2)
balmy root
mb it was -2tan(pi/4-x/2) -x+c
After editing, this is correct
woven nymph
now notice tan(pi/2-x) = cot(x)
hold on
u gotta lock tf in beceose what im about to do is very complicated
woven nymph
this beceoms tan^2(pi/4-x/2)
in ts step
woven nymph
u write it as tan(pi/4 - x/2) tan(pi/4 -x/2)
woven nymph
u write it as tan(pi/4 - x/2) tan(pi/4 -x/2)
convert one into cot
gray bridge
Yes? I use differentiation calculator and then sub x=0.1 to check
What are you talking about? "Differentiation calculator"? "Sub x=0.1"?
woven nymph
cot(pi/2 - pi/4 +x/2) tan(pi/4 - x/2)
now we have
tan(pi/4 - x/2)/ cot(pi/4 +x/2)
now convert it into sin cos
sin(pi/4 -x/2) cos(pi/4 +x/2) / sin(pi/4 +x/2) cos(pi/4 -x/2)
gray bridge
How do you take a definite integral?
woven nymph
multiply 2 to deno and numerator
gray bridge
Wait, hold on, what even is this?
woven nymph
then use the formula 2sin(a)cos(b) = sin(a+b) + sin(a-b)
balmy root
What are you talking about? "Differentiation calculator"? "Sub x=0.1"?
Oh, I see it wrong, I thought you are asking whether it is same after differentiation
woven nymph
sin(pi/4 -x/2) cos(pi/4 +x/2) / sin(pi/4 +x/2) cos(pi/4 -x/2)
so u reduce it into something like
sin(pi/2) - sin(x) / sin(pi/2) + sin(x)
which is the queiston given
hence it is correct
gray bridge
But there’s a question, if we’re doing definite integration, this will also lead...
This is what you said that we're discussing.
woven nymph
But there’s a question, if we’re doing definite integration, this will also lead...
do you wanna know how to convert the answer you got into teh anser given in the question?
balmy root
This is what you said that we're discussing.
I tried to use x=pi/3 sub them into both of two of different answers, eventually get two different answers
And the difference is 2
balmy root
hence it is correct
thanks, I’ll think about this proof
woven nymph
I tried to use x=pi/3 sub them into both of two of different answers, eventually...
who told you that putting values in 2 differnt antiderivativ of same quesiton will give same answer
the constant of 2 antiderivates need not be same
balmy root
If we’re considering definite integration, from 0 to pi/3
gray bridge
I tried to use x=pi/3 sub them into both of two of different answers, eventually...
Do you even know the fundamental theorem of calculus?
woven nymph
so the ocnstant gets canceled out
balmy root
yeah then it will be
Oh, I understand now, that would be canceled
balmy root
Do you even know the fundamental theorem of calculus?
definite integrals : f(a)-f(b)
thanks!
gray bridge
definite integrals : f(a)-f(b)
No.
woven nymph
what is f
balmy root
When integrating f’(x)
gray bridge
The precise statement of the fundamental theorem of calculus is the following; for f continuous on [a, b]:
- If d/dx(F(x)) = f(x), then int(a, b) f(x) dx = F(b) - F(a).
- If F(x) = int(a, x) f(t) dt, then d/dx(F(x)) = f(x).
balmy root
The precise statement of the fundamental theorem of calculus is the following; f...
thanks!
woven nymph
i highly doubt u understood anything but wtv
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@balmy root
balmy root
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