Practice question · Numerical answer
Define F(x) as the definite integral of t^2 from t = 0 up to t = x. Using the first part of the theorem, compute F'(3).
Hints
- You do not need to evaluate the integral at all.
- The derivative of the accumulation function is simply the integrand evaluated at the upper limit.
Show the answer
9
Why
F'(x) = x^2, so F'(3) = 9. Evaluating F(3) = 9 as well is a coincidence of this integrand; the point is that differentiating an accumulation gives the height back with no integration performed.
Practise The Fundamental Theorem of Calculus
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