If a on the interval [a,b] is a function instead of a constant, can you still apply the f.t.c? For example if a were sin(t) instead of a, would it work?
I'm doing a question where I need to find d/dt (sin(t) ? t² [sqrt(x^3 + 1)]dx)
(the derivative of the definite integral from sin(t) to t² of the square root of x cubed plus 1.)
We haven't learned how to find the antiderivative of sqrt(x^3 + 1) yet, so I'm guessing there must be another way to do it? Since all values of either sin(t) and t² are in the domain of sqrt(x^3 + 1), then am I allowed to apply the f.t.c [giving me sqrt(t^3 + 1) as the final answer]? or does "a" need to be a constant?
Thanks!
I'm doing a question where I need to find d/dt (sin(t) ? t² [sqrt(x^3 + 1)]dx)
(the derivative of the definite integral from sin(t) to t² of the square root of x cubed plus 1.)
We haven't learned how to find the antiderivative of sqrt(x^3 + 1) yet, so I'm guessing there must be another way to do it? Since all values of either sin(t) and t² are in the domain of sqrt(x^3 + 1), then am I allowed to apply the f.t.c [giving me sqrt(t^3 + 1) as the final answer]? or does "a" need to be a constant?
Thanks!