Evaluate the integral: $\displaystyle \int\frac{\sqrt{{{81}-{x}^{{2}}}}}{{{13}{x}^{{2}}}}{\left.{d}{x}\right.}$

(A) Which trig substitution is correct for this integral? (B) Which integral do you obtain after substituting for $\displaystyle {x}$ and simplifying?
Note: to enter $\displaystyle \theta$, type the word theta.
$\displaystyle \int$ $\displaystyle {d}\theta$
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(C) What is the value of the above integral in terms of $\displaystyle \theta$? (Hint: Use the identity $\displaystyle {{\cot}^{{2}}\theta}={{\csc}^{{2}}\theta}-{1}$)
+ C
Preview Question 6 Part 3 of 4  

(D) What is the value of the original integral in terms of $\displaystyle {x}$?
+ C
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