Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. If f is continuous on [a,b], then ddx(abf(x)dx)=f(x)
The given statement is true or false.
Recall theFundamentaltheorem of calculus part 1:
If is continuous on , then the function defined by is continuous on and differentiable on , and
Here the upper limit oftheintegration in variable is not a constant number.
If both limits on integration are constant numbers, then the integral is constant. Since derivative of constant is zero, answer must be zero.