Express the indeﬁnite integral sin(x^2) dx
as a power series

Question

anonymous · Answer

x^3/ 3 - x^7 /3!7 + x^11/5!11.....

anonymous · Answer

sin x = x - x^3/3! + x^5/5!....
so replace x by x ^2 and then integrate on the rhs

anonymous · Answer

understood?

anonymous · Answer

wat?? no..sry jus learning these..i hav no idea wats goin on..

anonymous · Answer

u can use taylors theorem to expand any function as a polynomial series...
the expansion of sin x is wht i wrote above...
if u replace x by x^2 on both sides u get the expansion of sin(x^2)
now multiply both sides by dx and integrate
LHS is integral sin(x^2)dx
and RHS u can find out by integrating each term

anonymous · Answer

$$f(x)= \sum_{0}^{\infty}a _{n}x ^{n}$$

anonymous · Answer

$$a_{n} = f^{(n)}(0)/ n!$$

anonymous · Answer

this is called a maclaurin series expansion

anonymous · Answer

understand now

anonymous · Answer

hm yea..makes better sense, its gonna take me a few problems to get fully get it but thanks!

anonymous · Answer

welcome....practice the expansions and ul be fine