Asked by Beth
Find the arc length of y = x^4 from the origin to (1, 1). Answer in length units, correct to two decimal places, please.
Answers
Answered by
MathMate
The integral required is:
I=∫sqrt(1+f'(x)^2)dx from 0 to 1
=∫sqrt(1+(4x^3)^2)dx from 0 to 1
An analytic result involves elliptic integrals. Numerical integration would therefore be recommended.
I=1.600... (to 3 decimal places)
I=∫sqrt(1+f'(x)^2)dx from 0 to 1
=∫sqrt(1+(4x^3)^2)dx from 0 to 1
An analytic result involves elliptic integrals. Numerical integration would therefore be recommended.
I=1.600... (to 3 decimal places)
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