EXAMPLE 3 Express the definite integral int_3^7 (x^(2)-1)dx as a limit of Riemann sums. Solution We have int_3^7 (x^(2)-1)dx= lim_(n- infty )((x_(0)^(2)-1)+(x_(1)^(2)-1)+cdots+(x_(n-1)^(2)-1))w where w=(4)/(n) and x_(0)=3,x_(1),x_(2),dots,x_(n)=7 all divide the interval 3,7 up into n even subintervals, all of width w.

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EXAMPLE 3 Express the definite integral  int_3^7 (x^(2)-1)dx as a limit of Riemann sums. Solution We have  int_3^7 (x^(2)-1)dx= lim_(n-> infty )((x_(0)^(2)-1)+(x_(1)^(2)-1)+cdots+(x_(n-1)^(2)-1))w where w=(4)/(n) and x_(0)=3,x_(1),x_(2),dots,x_(n)=7 all divide the interval 3,7 up into n even subintervals, all of width w.

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