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Chapter 6: Q. 50 (page 499)

Each definite integral represents the arc length of a function f(x) on an interval [a, b]. Determine the function and interval.

鈭�021+36xdx

Short Answer

Expert verified

The function is fx=4x3/2and interval is a,b=0,2.

Step by step solution

01

Step 1. Given information.

Consider the given function is鈭�021+36xdx.

02

Step 2. Use arc length formula. 

The formula for a function to find the arc length from x=ato x=bis given by鈭�ab1+f'x2dx.

03

Step 3. Find derivative of given function.

Compare given definite integral function with the arc length formula.

鈭�ab1+f'x2dx=鈭�021+36xdx=鈭�021+6x2dx


Therefore the derivative function isf'x=6xand the interval is0,2.

04

Step 4. Find function fx.

The function whose differentiation is 6xis fx=4x3/2.

Thus the required function isfx=4x3/2and the interval isa,b=0,2.

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