Homework SourseDo the following for the curve y4x2 on 02 a set up an integr
Do the following for the curve y=4x^2 on [0,2]
a. set up an integral for the length of the curve
b. use your grapher\'s or computers integral evaluator to find the curves length numerically.
please explain
a. set up an integral for the length of the curve
b. use your grapher\'s or computers integral evaluator to find the curves length numerically.
please explain
Solution
arc length = integral of (1+y\'^2)dx....limit from 0 to 2
y = 4x^2
y\' = 8x
arc length = integral of (1+64x^2)dx
arc length = 1/8 integral of (1/64 + x^2)dx
integral of (a^2 + x^2)dx = x/2 (a^2+x^2) + a^2/2 ln|x + (a^2+x^2)
applying formula
arc length = 1/8 [x/2 (1/64 + x^2) + 1/128 ln|x + (1/64+x^2)
apply limits
arc length = 1/8[(1/64 + 4) + 1/128 ln|2+(1/64 + 4)] - 1/128 ln|(1/64)
arc length = 1/8[257/256 + 1/128 ln|2+257/256| - 1/128 ln|1/8|
![Do the following for the curve y=4x^2 on [0,2] a. set up an integral for the length of the curve b. use your grapher\'s or computers integral evaluator to find](/WebImages/36/do-the-following-for-the-curve-y4x2-on-02-a-set-up-an-integr-1106837-1761585995-0.webp "Do the following for the curve y=4x^2 on [0,2] a. set up an integral for the length of the curve b. use your grapher\'s or computers integral evaluator to find")
