Assume that sin(x) equals its Maclaurin series for all x. ?

Question

Assume that sin(x) equals its Maclaurin series for all x. Use the Maclaurin series for sin(2x^2) to evaluate the integral

int[0,.62](sin(2x^2)dx)

Your answer will be an infinite series. Use the first two terms to estimate its value.

Answer 1

Maclurin Serious has a C = 0

So, it makes the problem a lot easier

The serious goes something like this..

f(x) + f'(x)x + f''(x)x^2/2! + f'''(x)x^3/3! ......

f(x) = sin2x^2

f'(x) = 4sin2xcos2x

f''(x) = 4(2cos2x^2 + 2sin2x^2) = 8(2) = 16

Okay, someting like that..And once you find the deravatives, you plug it into the give Formula

f(x) + f'(x)x + f''(x)x^2/2! + f'''(x)x^3/3! ......

After that, I forgot..Sorry.  I'm pretty sure, it looks something like above.