Applications of the Integral

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

Solution for Problem 1 >>

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

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

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Problem : Find the length of the graph of g(x) = 2x ^3/2 from x = 2 and x = 5 .

Solution for Problem 2 >>

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

9 dx	=	u 1/2 du
	=	|19 46
	=	(463/2 -193/2)

or approximately 16.98 .

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