Question

Please show work clearly! will give a thumbs up!

3. ( Practice ) Our goal is to find the arc length of the spiral r = 0 from 0 <O<1. (a) Using techniques from Trigonometric Integrals, show that the following integral equality holds: I sec r tandx = = / secx dx - Insec +tangl. 1/4 0 (b) Using Integration By Parts and part (a), evaluate secs x dx. Hint: let u = sec. in the IBP. (c) Use the previous parts to find the arc length of the spiral r = from 0 <0 <1. I

Answer 1

Jseen seentana da 3 = [seca (le seizzada see&dx-(seende see xdx- /seekda seenda - Sseex case đa < x < 3+ena dº (seext tony Now Let seek tann du = (deen tamet see u- Lu hence du - Intal ſ seen du =S. lnl secastanal Thus we write I seextañada S suzdr– kn/semestern see?n du my 6) s ט Let ze= şeen de- seentana du da du Secafann da efer? they } u.de Zalzê-l dh ( ūdu ali_1 VE √2 W_141) du Truri TE du Toidu Tul ={{4722-1 – lu cheitern + ln Tuntu} 1 [ufze-1 + ln Zurious 1 12+ lu (+12-o - T2 + er leve) 2 -In 1-1478 (e 8= are length 24 dr todo W te do cdr do _Now dr=d do 2= finito ltor do het o=tana do = seinda tly 3 See da L- n S un ring L = 1.1478 the value of the integration I seen dre=1.1478 Jo