Antidiff question

[b^3]

Ok guys I've honestly got no clue here. This is off a Insight Exam, Exam 1 so no calculator.
Remember to keep it within the VCE Spesh course.

Question 7
Given and y=1 when x=0. (NOTE: that is NOT a typo)
Find the value of y when .
Worth 4 marks.
First step of the solution, they give
Final answer is
 

[acinod]

Just solve the differential equation to find y(x) and then find y(root3).

To integrate that, let x=sin(u)/2.

You'll notice that 1-4x^2 turns into 1-sin^2(u) and if u root that u just get cos^2(u). And from there you can just do the standard integration techniques for solving trig.

[b^3]

OK so I just want to make sure I get this. We want something to replace the 1-4x² so that it becomes integratable (I don't think that is a word)? So that means we try to make the 1-4x^2 into a trig function? Yes? I think I get what you mean, I just don't know how you saw that.

[b^3]

Ok I'm still not quite there yet, could you show a little bit of working? please?

[brightsky]

google search trig substitution.

[pi]

OK so I just want to make sure I get this. We want something to replace the 1-4x² so that it becomes integratable (I don't think that is a word)? So that means we try to make the 1-4x^2 into a trig function? Yes? I think I get what you mean, I just don't know how you saw that.

Yes, its trigonometric substitution. For that example, (sinu)/2 was the best bet (or (cosu)/2) for the pythagorean identity.

[acinod]

Ok I'm still not quite there yet, could you show a little bit of working? please?

Click the show steps button: http://www.wolframalpha.com/input/?i=integrate+%282x^2%29*%281-4x^2%29^1%2F2

[b^3]

Ok I'm still not quite there yet, could you show a little bit of working? please?

Click the show steps button: http://www.wolframalpha.com/input/?i=integrate+%282x^2%29*%281-4x^2%29^1%2F2

Lol, Exaclty what I was doing.

[Andiio]

For some reason I thought trig substitution wasn't on the course, :|