(Solved): Use a change of variables to evaluate the following definite integral. \[ \int_{-1}^{0} x \sqrt{1- ...

Use a change of variables to evaluate the following definite integral. \[ \int_{-1}^{0} x \sqrt{1-x^{2}} d x \] Determine a change of variables from \( x \) to \( u \). Choose the correct answer below. A. \( u=2 x^{1} \) B. \( u=x^{2} \) C. \( u=\sqrt{1-x^{2}} \) D. \( u=1-x^{2} \) Write the integral in terms of \( u \). \[ \int_{-1}^{0} x \sqrt{1-x^{2}} d x=\int_{0} 1 \mid d u \] Evaluate the integral. \[ \int_{-1}^{0} x \sqrt{1-x^{2}} d x= \] (Type an exact answer.)