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VA 8.1 Homework-Arc Length - 20 x X Mathway | Algebra Problem Sol X Smarthinking Free Tutoring X Smarthinking Free Tutoring + C webassign.net/web/Student/Assignment-Responses/submit?dep=27084291&tags=autosave#question4913935_1 # R Paused EXAMPLE Find the arc length for the curve y = 4x2 - _ In(x) taking Po(1, 4) as the starting point. SOLUTION If f(x) = 4x2 - - In(x), then f' (x) = 8x - 1 32x 1 + [f 1 + [f'(x) ]2 p> ' ( x ) 1 2 8x - 32x = 1 + 64x2 - 0.5 + 1024x2 = 64x2+ 0.5 + 1024x2 64x-+ 0.5+ 1024x V 1 + [f ' ( x) 12 1/64x2 + 0.5 + - 1024x Thus the arc length is given by s ( x ) = / V 1 + [ f ( t ) 1 2 dt 6412 + 0.5 + 10247 9 For instance, the arc length along the curve from (1, 4) to (2, f(2)) is s(2) = 10 + In(2) - 4 = 11 + In(2) 32 12 (rounded to four decimal places) Submit Answer 3. [-/1 Points] DETAILS SCALCET9 8.1.001. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the arc length formula to find the length of the curve y = 3 - 4x, -1 s x S 2. Check your answer by noting that the curve is a line segment and calculating its length by the distance formula