Calculus Problem Helpp?

Question

I did this before but I forgot how to do calculus problems like these. The question tells me to use the fundamental theorem to find h'(x) , given h(x) = integral of (7+r^3)^1/2 from intervals X^2 to 0

Answer 1

The fundamental theorem of calculus states that

If f is continuous on [a,b] then is continuous on [a,b] and differentiable on (a,b) , with derivative f(x) .

Here we cannot directly apply the fundamental theorem, because the upper limit of integration is x² , not x. Instead, we must use the chain rule .

Let u = x² 

So