Easy trig integral =/
I haven't done any sort of trig integrals in the past and i have pretty much forgotten all my identities since i haven't looked at them for over 3 years so please bear with me.
The question is:
upper limit = 1, lower limit = 0.
Integrate cos (x^2) with those bounds.
First off I had to approximate the integral using the midpoint/trapezoidal rules. Those were fairly straightforward. Now i want to check my answer but I'm kinda lost.
If i took the integral of cos (x^2), i would get sin(x^2) no?
Subbing in the limits of integration i would get sin(1) - sin(0) = sin (1)
but using the approximation rules above I got the integral as being approximately equal to one, which does not equal to sin (1).
The integral of cos(x^2) cannot be found in closed form using elementary functions.
Originally Posted by Kuma
Thanks. But how would i differentiate that then? Does chain rule apply or something. I've never worked with trig functions before so. I do know that d/dx cos x = sin x, how would that apply to cos x^2?
Yeah, you use the chain rule. First, find the derivative of sin, then find the derivative of the value within sin.
Ah i see. So you can differentiate cos x^2 to get 2x sin x^2, but the integral of that would pretty much be impossible to find. Makes sense.
I find that .
(Not that it's significant or matters, anyway).