find derivative of the given function....?

Question

find derivative(g*(x)) of given function

g(x)=nInt(t*(sq root of(t^3+2t))dt),x,x,-1)

i.e. function is= t*(sq.root of (t^3+2t)
up limit=x
lower lim=-1
nint= integral sign like "S"

Answer 1

This is a fundamental theorem of calculus problem.

The derivative of the integral of t * sqrt (t^3 + 2t) dt from -1 to x is

x * sqrt (x^3 + 2x)

Answer 2

shouldn't the derivative of an integral just be the function....

F(x) = x^2
integral is X^3 / 3 + C
derivative of that is x^2
Even if you integrate that. YOU will get the original function with the X's integrated and then some constants...that just go to zero when the derivative is taken.

Answer 3

The usual way of writing the square root of something is to use either sqrt(x) or x^(1/2). The first answerer did the rest of it.

Answer 4

Use integration by parts for t*V(t^3 + 2t) , taking t as u in the formula

int. u.(dv/dx) dx = uv - int. v.(du/dx) dx

with dx replaced by dt, then plug the boundaries.