By means of the substitution y = kcosx, where k is a positive constant, evalute the integral (1/2 integral sign 0) [y^2 / sqrt(1-4y^2)] dy, giving your answer in exact form.
Gonna erase a hole in the paper but still dunno how to do. Please help. Thank you!
subst every thing in , take care of the dx, differentiate the substitution, find the relationship between dy and dx, express dx in the form of a function with dy, replace dx with the dy, afterwards, cancel any like factors, limits also take note, find the relationship bet 0.5 and y, subst into y=kcosx, which the upper limit is kcos0.5. den see
Originally posted by sushinut:Yeah I kinda did that but than I would get…
cos-1(1/2k) integral sign π/2 * (-ksinx) dx
Then I don’t know how to integrate.
Lazy to check, I will assume your integral is correct.
Integrate -ksinx will give you kcosx.
kcos(cos^-1(1/(2k)) - kcos(pi/2)
=1/2-0
=1/2
Hi,
Let k = 1/2 when the substitution is used.
Notice that sqrt(1 - 4y^2) becomes sqrt(1 - cos^2 x), which simplifies to sin x.
Thanks.
Cheers,
Wen Shih