Calculus I · Antiderivatives, definite integrals, and the Fundamental Theorem of Calculus
Differentiate an accumulation function with a variable upper bound
Problem
Let $G(x)=\displaystyle\int_1^{x^2}\sqrt{1+t^3}\,dt$. Find $G'(x)$ and $G'(0)$. Explain why it is unnecessary to find an elementary antiderivative of $\sqrt{1+t^3}$.
Hint
Name the mathematical object that changes or is sought, and record the domain before doing algebra or calculus.
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