Definite Integration
General
Grade 12
Question:
If $F(x) = \int_{x}^{x^2} \sqrt{\tan t} dt$, then find $F'(x)$.
Step-by-Step Solution
Key Concept: General
$$F'(x) = \frac{d}{dx} \int_{x}^{x^2} \sqrt{\tan t} dt = \sqrt{\tan(x^2)} \cdot \frac{d}{dx}(x^2) - \sqrt{\tan x} \cdot \frac{d}{dx}(x)$$ $$= 2x \cdot \sqrt{\tan x^2} - 1 \cdot \sqrt{\tan x}$$
Correct Answer: A