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Applications of the Integral

Math

Problems 4

Summary Problems 4

Problem : Find the length of the graph of f (x) = (1/2)(ex + e-x) from x = 0 to b.

Since f'(x) = (1/2)(ex - e-x), the length of the graph is equal to


dx=ex + e-xdx  
 =(ex - e-x|0b)  
 =  

Problem : Find the length of the graph of g(x) = 2x3/2 from x = 2 and x = 5.

Since g'(x) = 3, the length is given by dx. Making the change of variables u = 1 + 9x, we have


9dx=u1/2du  
 =|1946  
 =(463/2 -193/2)  

or approximately 16.98.