Definite Integration
General
Grade 12
Question:
If $F(x) = \int_{x^2}^{x^3} \frac{1}{\ln t} dt$ then find $F'(e)$.
Step-by-Step Solution
Key Concept: General
$$F'(x) = \frac{3x^2}{\ln x^3} - \frac{2x}{\ln x^2} = \frac{x^2}{\ln x} - \frac{x}{\ln x} = \frac{x(x-1)}{\ln x}$$ $$now \ F'(e) = \frac{e(e-1)}{\ln e} = e(e-1)$$
Correct Answer: e(e-1)