APMA 1110 Final questions with verified solutions

APMA 1110 Final

ILATE - correct answer ✔✔Inverse trig, log, algebraic, trig, exponential



sinx is odd - correct answer ✔✔u=-cosx



cosx is odd - correct answer ✔✔u=sinx



cosx is even, sinx is even - correct answer ✔✔trig identity



1. cos^2(x)= - correct answer ✔✔(1+cos2x)/2



2. sin^2(x)= - correct answer ✔✔(1-cos2x)/2



secx is even - correct answer ✔✔u=tanx



secx is odd and tanx is odd - correct answer ✔✔u=secx



Int(tanx)= - correct answer ✔✔ln|secx|+C



Int(secx)= - correct answer ✔✔ln|secx+tanx|+C



√a^2-x^2 - correct answer ✔✔x=asin@



√a^2+x^2 - correct answer ✔✔x=atan@



√x^2-a^2 - correct answer ✔✔x=asec@

, 2. cos^2(x)= - correct answer ✔✔1-sin^2(x)



2. sec^2(x)= - correct answer ✔✔1+tan^2(x)



tan^2(x)= - correct answer ✔✔sec^2(x)-1



sin(2x)= - correct answer ✔✔2sinxcosx



int(b^x) - correct answer ✔✔b^x/lnb



deltax/3, deltax= - correct answer ✔✔b-a/n



E< or = - correct answer ✔✔K(b-a)^5/180n^4



int(A/(x+a)) - correct answer ✔✔Aln|x+a|+C



int ((Ax)/(x^2+a)) - correct answer ✔✔(A/2)ln(x^2+a)+C



int(A/(x^2+a^2)) - correct answer ✔✔(A/a)tan^-1(x/a)+C



arc length/ds - correct answer ✔✔int(√1+(dy/dx)^2)



surface area - correct answer ✔✔int(2pirds)



(x̄ , ȳ) - correct answer ✔✔(My/m, Mx/m)



Mx= - correct answer ✔✔1/2pint(f(x)^2)