Could somebody confirm or deny that I'm heading in the right direction by saying my next step would be 1/10((-1/2)cos(t^2) evaluated at 10, minus that evaluated at 0?
Are you sure you arent finding the average value of sin(t^2) on the interval [0,10] ?
Then the average value is:
then substitute u = t^2 and solve.
You should get around .0688.
If you are finding the average value of tsin(t^2), the average value is:
and this integral is now very difficult and involves the Fresnel integral. The value here is about -4.01.