Integration by substitution

[Sonal7]

I got this far but unsure whether it's a reverse chain rule Q

 

[Dr.Peterson]

You've done well so far, apart from an incorrect limit of integration.

My next step would be to split up the cube into sin(x) sin^2(x), and make another substitution. (You might be surprised at what that substitution is!)

Alternatively, you could have started differently, letting u = 1 - x^2. This will be more direct. I'd recommend trying both ways.

 

[Sonal7]

I recognised that the limit was wrong. I think I am getting there

 

[Sonal7]

I don't get it

 

[Sonal7]

Thats the right answer . I used reverse chain rule, and sub'd the values for the limits. Answer is 2/15. Thank you!

 

[Dr.Peterson]

I take it you fixed the sign error.

Did you try my suggestion, letting u = 1 - x^2 at the start?

 

[Sonal7]

I fixed the error sign! I haven't tried the other method yet. It would be a good way of checking a solution.

 

[Steven G]

Yes, you should try the other method but the best check is to take the derivative of the integral (before substituting the limits) to see if you get back the integrant