Evaluate the following integrals.

Chapter 4, Problem 32E

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QUESTION:

Evaluate the following integrals.

\(\int \frac{\sqrt{9-x^{2}}}{x^{2}} d x\)

Questions & Answers

QUESTION:

Evaluate the following integrals.

\(\int \frac{\sqrt{9-x^{2}}}{x^{2}} d x\)

ANSWER:

Problem 32E

Evaluate the following integrals.

                         dx.

Answer;

Step 1

          The given integral is  

         By  the substitution method we can evaluate the limit .

                     For our convenience  let , us take  x = 3 sin(p)  (or) x = 3 cos(p)

                       Let  x = 3 sin(p) , that implies  = sin(p) = , = cos(p) = , and tan(p) =  =  , cot (p)  = …………..(1)

   Then the integrand becomes =

         

                                                                 = , since = 9.

              &nb

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