calculate the arc length of the indicated portion of the curve r(t) r(t)=11t^4i+2t^4j+10t^4k 1

Question

calculate the arc length of the indicated portion of the curve r(t) r(t)=11t^4i+2t^4j+10t^4k 1<or=t<or=3

dumbcow · Answer

$$Arc = \int\limits_{1}^{3}\sqrt{1+r'(t)^{2}}dt$$
not sure what to do with the i,j,and k

anonymous · Answer

oh ok thanks for the guidence can you help with more

dumbcow · Answer

sure

anonymous · Answer

so i believe the equation to use here is L (arc length) = $$\int\limits_{1}^{3} [r'(t)]dt$$

anonymous · Answer

you want to find the derivatives of each i, j, and k... so (44t^3)i + (8t^3)k + (40t^3)k
after that you evaluate each function... sqrt((dx)^2 + (dy)^2 + (dz)^2)... this essentially squares the r'(t) vector components and puts it under the sqrt.

anonymous · Answer

after substituting and simplifying you should come out with 60t^3  *assuming i did all the algrebra right!* 
you then integrate it which becomes 15t^4...
finally you apply your limits so 15(3^4)-15(1^4) = 1200.