applestrudle said:Homework Statement
Find the length of the curve y = x^3/a^2 + a^2/12x
between a and a/2
Homework Equations
Length L = integrate (1+ dy/dx)^2)^0.5
The Attempt at a Solution
I got to
integrate (9x^4/a^2 + 1/2 + a^4/144x^4)^0.5
but I can't simplify it
LCKurtz said:Is that last term supposed to be ##\frac {a^2}{12x}## or ##\frac{a^2x}{12}##?Did you leave out the ##1##? It would help if you showed your work.
applestrudle said:integrate (9x^4/a^2 + 1/2 + a^4/144x^4)^0.5
A length of curve integral is a mathematical concept used to find the length of a curve on a graph. It involves breaking the curve into small segments and calculating the length of each segment using the Pythagorean theorem. The total length is then found by summing up all the segments.
To calculate a length of curve integral, you first need to determine the equation of the curve. Then, you divide the curve into small segments and use the Pythagorean theorem to find the length of each segment. Finally, you add up all the segments to get the total length.
A length of curve integral is important in various fields of science and engineering, such as physics, calculus, and geometry. It allows for the accurate measurement of curves and is used in the design and analysis of structures and systems.
No, a length of curve integral cannot be negative. The length of a curve is always a positive value, as it represents the distance between two points on the curve.
Yes, there are many real-world applications of a length of curve integral. It is used in fields like architecture, engineering, and physics to calculate the length of curved surfaces, such as bridges, roads, and pipes. It is also used in computer graphics to create smooth and realistic curves in 3D animations and designs.