APMA 1110 Test Review questions with complete solutions

APMA 1110 Test Review

Integration by parts - correct answer ✔✔∫ u dv = uv - ∫ v du



derivatives of sin, cos, and tangent (and sec) functions (6) - correct answer ✔✔d/dx sinx=cosx

d/dx cosx=-sinx

d/dx tanx=sec2x

d/dx sinu= cosu*u'

d/dx cosu= -sin(u)*u

'd/dx tanu = sec2u*u'

d/dx secx= secxtanx



derivatives of sec^2, cot, and csc functions - correct answer ✔✔d/dx sec^2x=tanx

d/dx -cotx= -csc^2x

d/dx -cscx= -cscxcotx



Derivative Rule for Inverses (arcsin, arccos, arctan) - correct answer ✔✔d/dx arcsinx = 1/rad(1-x^2)

d/dx arccosx = -(1/rad(1-x^2) )

d/dx arctan = 1/(1+x^2)



derivative of e and ln (4) - correct answer ✔✔d/dx e^x = e^x

d/dx e^f(x) = e^f(x) * f'(x)

d/dx lnx= 1/x

d/dx ln(f(x))= 1/f(x) * f'(x)



Anti-power rule - correct answer ✔✔(cx^n+1)/n+1

, Anti-chain rule substitution.

What things do you make the u? - correct answer ✔✔Make the u:

- something raised to a power

- something inside a trig function

- power of e

- denominator of a fraction



if the x doesn't cancel out when you are using a u substitution, what do you do? - correct answer
✔✔Take original u substitution and solve for x and plug x = in what hasn't been crossed out. Multiply u's
together and solve.



Antiderivative trig functions - correct answer ✔✔anti derivative of cosx: sinx

anti derivative of sinx: -cosx

anti derivative of -sinx: -cosx

anti derivative of sec^2x: tanx

anti derivative of secxtanx: secx

anti derivative of csc^2x: -cotx

anti derivative of tan^2x: tanx-x

anti derivative of tanx: ln|secx|



Antiderivative of e's and 1/x - correct answer ✔✔anti derivative of e is e

anti derivative of 1/x is ln|x|



Antiderivative of ln - correct answer ✔✔xlnx-x



antideriv of inverse sin - correct answer ✔✔xsin^-1x-∫x/(sqrt(1-x^2)



Choosing u - correct answer ✔✔Inverse

Log