Evalutate lim, x->0, int [0,x] [sin t^2] dt / x^2

[kimmy_koo51]

Evaluate the limit
lim Integral (upper limit x, lower limit 0) sin t^2 dt / x^2
x->0

 

[stapel]

Integral (upper limit x, lower limit 0) sin t^2 dt / x^2

Is the integrand either of the following?

. . . . .sin[sup:2tb74weg]2[/sup:2tb74weg](t) / x[sup:2tb74weg]2[/sup:2tb74weg]

. . . . .sin(t[sup:2tb74weg]2[/sup:2tb74weg]) / x[sup:2tb74weg]2[/sup:2tb74weg]

Or am I incorrect to assume that the x[sup:2tb74weg]2[/sup:2tb74weg] is actually contained within the integral, rather than dividing it?

When you reply, please include a clear listing of your thoughts and attempts so far. Thank you!

Eliz.

 

[kimmy_koo51]

Re: Evalutate lim, x->0, int [0,x] [sin t^2 / x^2] dt

i didnt type it clear enough the x^2 is not included in the integral, the entire integral is divided by x^2

lim integral / x^2
x-> 0

and the integral is _ x
/ sin t^2 dt
_/
0

When i first saw this the idea of the fundamental theorum of calculus came into my head, so i tried

F(x) = integral
F'(x) = sin x^2, but then i realized that we wanted to solve the integral, and not find the derivative of the answer, so i took the antiderivative of derivative i obtained

The integral then equalled : cos x - 1

does this make sense?

 

[kimmy_koo51]

Re: Evalutate lim, x->0, int [0,x] [sin t^2 / x^2] dt

the integral is from 0 to x of sin t^2 dt

NOT sin^2 t