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# A tale of two integrals watch

1. (Original post by Indeterminate)
Looks as though problem 2 has now been dealt with

A hint for problem 1
Spoiler:
Show

Notice that we can rewrite our integral as

and now there's some simplification that can be done

Ahh thanks for the hint but I got to that part yesterday.. I simplified the left part to (1-cosx)^2 all over sinx

I got stuck there :/
2. (Original post by Student403)
Ahh thanks for the hint but I got to that part yesterday.. I simplified the left part to (1-cosx)^2 all over sinx

I got stuck there :/
That's absolutely fine!

Here's another hint:
Spoiler:
Show
Weierstrass
3. (Original post by Indeterminate)
Looks as though problem 2 has now been dealt with

A hint for problem 1
Spoiler:
Show

Notice that we can rewrite our integral as

and now there's some simplification that can be done

Looks like it's down to me to wrap things up.

Solution 1

Letting denote our integral, and continuing from the above, we get

gives us

Now let to get

And so our solution in terms of is

4. (Original post by Indeterminate)
Looks like it's down to me to wrap things up.

Solution 1

Letting denote our integral, and continuing from the above, we get

gives us

Now let to get

And so our solution in terms of is

Oh my god I would never have got that
5. (Original post by Student403)
Oh my god I would never have got that

But these integrals were far from easy and, given the lack of guidance, more difficult than any STEP II question on the topic
6. (Original post by Indeterminate)

But these integrals were far from easy and, given the lack of guidance, more difficult than any STEP II question on the topic
Thanks for the encouragement Don't worry - it was definitely fun to try!

I think one of my main weaknesses (which many STEP takers seem to be great at) is choosing my own substitutions to make. Ah well - hopefully that will improve with time and practice
7. (Original post by Student403)
Thanks for the encouragement Don't worry - it was definitely fun to try!

I think one of my main weaknesses (which many STEP takers seem to be great at) is choosing my own substitutions to make. Ah well - hopefully that will improve with time and practice
Yes, practice makes perfect!
8. (Original post by Indeterminate)
Yes, practice makes perfect!
Thank you for the thread I will be sure to try harder in the next one!
9. (Original post by Student403)
Thank you for the thread I will be sure to try harder in the next one!
Glad you liked it Next time, I think I'll post a few problems that concern other areas of Maths (just for the sake of variety), as well as a couple of integrals!
10. (Original post by Indeterminate)
Glad you liked it Next time, I think I'll post a few problems that concern other areas of Maths (just for the sake of variety), as well as a couple of integrals!
Sounds good!

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