APMA 1110 Final Questions and Correct Answers

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APMA 1110 Final Questions and Correct
Answers
ILATE Ans: Inverse trig, log, algebraic, trig, exponential

sinx is odd Ans: u=-cosx

cosx is odd Ans: u=sinx

cosx is even, sinx is even Ans: trig identity

1. cos^2(x)= Ans: (1+cos2x)/2

2. sin^2(x)= Ans: (1-cos2x)/2

secx is even Ans: u=tanx

secx is odd and tanx is odd Ans: u=secx

Int(tanx)= Ans: ln|secx|+C

Int(secx)= Ans: ln|secx+tanx|+C

√a^2-x^2 Ans: x=asin@

√a^2+x^2 Ans: x=atan@

√x^2-a^2 Ans: x=asec@

2. cos^2(x)= Ans: 1-sin^2(x)


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2. sec^2(x)= Ans: 1+tan^2(x)

tan^2(x)= Ans: sec^2(x)-1

sin(2x)= Ans: 2sinxcosx

int(b^x) Ans: b^x/lnb

deltax/3, deltax= Ans: b-a/n

E< or = Ans: K(b-a)^5/180n^4

int(A/(x+a)) Ans: Aln|x+a|+C

int ((Ax)/(x^2+a)) Ans: (A/2)ln(x^2+a)+C

int(A/(x^2+a^2)) Ans: (A/a)tan^-1(x/a)+C

arc length/ds Ans: int(√1+(dy/dx)^2)

surface area Ans: int(2pirds)

(x̄, ȳ) Ans: (My/m, Mx/m)

Mx= Ans: 1/2pint(f(x)^2)

My= Ans: pint(xf(x))

Parametric Arc Length (distance/ds) Ans:
int(√(dx/dt)^2+(dy/dt)^2)

Parametric speed Ans: √(dx/dt)^2+(dy/dt)^2



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