One of the best approach and explanation to the problem. It helped me to clear my doubts. I never wondered solving the problem with trigonometric substitution. A wonderful video🙏
It's worth considering the "restrictions" that you keep mentioning in light of the domain of the integrand: [0,1). From the start, you're never going to encounter a negative sine value. I don't know if that's all that needs to be considered, though. It's nice to see, however, that whenever we use trig substitutions, the integrand tends to have a compliant domain, at least as far as I've noticed. These things are tricky and I tend to believe that the spirit of the syllabus - and what I can reasonably achieve with my students - is the various integration tricks without being too picky.
One of the best approach and explanation to the problem. It helped me to clear my doubts. I never wondered solving the problem with trigonometric substitution. A wonderful video🙏
It's worth considering the "restrictions" that you keep mentioning in light of the domain of the integrand: [0,1). From the start, you're never going to encounter a negative sine value. I don't know if that's all that needs to be considered, though. It's nice to see, however, that whenever we use trig substitutions, the integrand tends to have a compliant domain, at least as far as I've noticed.
These things are tricky and I tend to believe that the spirit of the syllabus - and what I can reasonably achieve with my students - is the various integration tricks without being too picky.
Thank you air
Thx
I don't understand how cos(2x)=1-2sin^2(x), wouldn't it be cos(2x)=sqrt(1-sin^2(2x))?
Both of the things you have stated are true, the first just relates the "2x" world (functions of 2x) to the "x" world.