Integrals of form $\int (\sqrt{ax^2 + bx + c}) dx$
General
Grade 12
Question:
Evaluate $\int \sqrt{5 - 4x^2} dx$
Step-by-Step Solution
Key Concept: General
Using the formula $$\int \sqrt{a^2 - x^2} dx = \frac{x}{2} \sqrt{a^2 - x^2} + \frac{a^2}{2} \sin^{-1} \frac{x}{a} + C$$, we get $$\int \sqrt{5 - 4x^2} dx = \frac{1}{4} \left( 2x \sqrt{5 - 4x^2} + 5 \sin^{-1} \left( \frac{2x}{\sqrt{5}} \right) \right) + C$$
Correct Answer: A