Supposethata,bRand0t.Letxa=(ba)sin2t. 2 lving the lemniscate ay find the following i) Show that ii) Use the substitution x a = (b a) sin2 t to...

Supposethata,b∈Rand0≤t≤π.Letx−a=(b−a)sin2t. 2

lving the lemniscate ay find the following

i) Show that ii) Use the substitution x − a = (b − a) sin2 t to evaluate the integral

b−x = (b−a)cos2 t. ∫1

√ dx, a<x<b.