Question

1. Find the length of the curve x = 13 – 6t2, y = + + 6t2, t€ (0,1).

Answer 1

The length of u= f(t) , y = g(t) enterval [a, b] is given by length of a curve of the form the closed on t=6 7. 1)? It t=a We ,7= €²642 Now, have, H = £² 622 diff. a and У with res respect to t, we get du d t - 6t dt dt d not at at It } t = 622) (+3) – 6.d 3t2 12t 2 at (3+2 122) 2 =94_723 + 144t2 (a-b)? arrab +62 Now, dy at at -34 t +622) lt')+ 6.64() It It 2 = 3t + 6x2t = 3724127 dy)? (3t+12+) 4 - 9+72+14+ (a+b)? - azt hab +62
The answer sheet has three pages.it is the first page
ceine on Thus, the length of the given [0, 1] is given by V (92 - 724 + 144+²)+ (a1 + 722 +1442%24 t=1 3. t=0 ✓ 18t² + 14422 18th(+218) at o t. ✓ 2278 at = √18 0 cer make substitution, +2+8=22 .. tit = 2202 i tot = Zdz and t Z √8 3 have, Thes 3 18 ſz? zde 3 - T8 22 dz 158
second page
3 8 3 sont to 32 VTS [zd? [2] 10 (8) ntl r8 3√2 3 √2 [27 - 8x88 = V2 [27 - 8x252 272-32 6.1837 - 6.18 Korrect cepto two deciman places, Therefore, the length of the given curve t Eto, 1) is is on 6.18 units.
Third/last page