(Solved): Evaluate the following integral using trigonometric substitution. \[ \int_{0}^{\frac{\sqrt{3}}{2}} ...

Evaluate the following integral using trigonometric substitution. \[ \int_{0}^{\frac{\sqrt{3}}{2}} \frac{x^{2}}{\sqrt{1-x^{2}}} d x \] What substitution will be the most helpful for evaluating this integral? A. \( x=\sec \theta \) B. \( x=\sin \theta \) C. \( x=\tan \theta \) Rewrite the given integral using this substitution. \[ \int_{0}^{\frac{\sqrt{3}}{2}} \frac{x^{2}}{\sqrt{1-x^{2}}} d x=\int_{0} 1 \mid d \theta \] (Simplify your answers. Type exact answers.)