MX2 Integration Marathon (1 Viewer)

stupid_girl

Active Member
Joined
Dec 6, 2009
Messages
221
Gender
Undisclosed
HSC
N/A
For this integral, some trig identities may make your life easier. Of course, Weierstrass substitution will also work.




 

stupid_girl

Active Member
Joined
Dec 6, 2009
Messages
221
Gender
Undisclosed
HSC
N/A
#83 and #88 are still outstanding and this is a new one.
Feel free to share your attempt.
It seems no one has attempted yet. This one is a little bit interesting.
At the first glance, everything is related to 4^x so it makes sense to substitute u=4^x to get


If you put these two functions for 1<u<4 in a graphing software, you should be able to sense what's going on.



The area should add up to a 3x3 square, ie.
 
Last edited:

Drdusk

Moderator
Moderator
Joined
Feb 24, 2017
Messages
2,025
Location
a VM
Gender
Male
HSC
2018
Uni Grad
2023
She needs to change her name. The irony is so real...
 

HeroWise

Active Member
Joined
Dec 8, 2017
Messages
353
Gender
Male
HSC
2020
Funny thing is i only got out like 3 of them out and sacked the rest.

Yeah we are the stupid ones ahha
 

stupid_girl

Active Member
Joined
Dec 6, 2009
Messages
221
Gender
Undisclosed
HSC
N/A
This is a rather tough one...especially the final simplification. Feel free to share your attempt.
 

fan96

617 pages
Joined
May 25, 2017
Messages
543
Location
NSW
Gender
Male
HSC
2018
Uni Grad
2024
For , let



Prove that



Given that



Show that



 

Daniel.22

New Member
Joined
Jun 26, 2019
Messages
6
Gender
Male
HSC
2022
This is a rather tough one...especially the final simplification. Feel free to share your attempt.
It is just tedious...

Edit: Sorry, typoed the numerator of the second integral in the second line of the evaluation of I, should just be cos(2x).

26866
 
Last edited:

Daniel.22

New Member
Joined
Jun 26, 2019
Messages
6
Gender
Male
HSC
2022
For , let



Prove that



Given that



Show that



I'll leave the intended solution for someone else to write out (p.s I think you need to be a bit careful about the first part, the integrals are indefinite so equality will only hold up to a constant as written.)

A cute alternate solution (but I don't believe this technique is allowed in MX2):

26867
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top