MATH 2414 Exam 2 Questions And Complete
Solutions (Verified Solutions) 2026
Integration by parts formula - CORRECT ANSWER -∫ udv = uv − ∫ vdu
When to use integration by parts - CORRECT ANSWER -when there are two distinct function
multiplied together
LIPET - CORRECT ANSWER -rule of thumb for choosing u; logs, inverse trig, polynomials,
exponential, and trig
What happens if you perform integration by parts and are left with another product - CORRECT
ANSWER -do it again
What to do if you perform integration by parts multiple times, but end up with the same thing as
your og function - CORRECT ANSWER -make this "y" and solve for it
Helpful int by parts tip - CORRECT ANSWER -a possible route is making the entire function u,
and dv dx. Mainly intended to set up easier u sub
Necessary trig identities - CORRECT ANSWER -sin2(t) + cos2(t) = 1
Tan2(t) + 1 = sec2(t)
1 + cot2(t) = csc2(t)
Integral of e^2x dx - CORRECT ANSWER -1/2e^2x + C; reciprocal of coefficient
Derivative of e^2x - CORRECT ANSWER -2e^2x
Simple strategies for trig integrals - CORRECT ANSWER -substitution and multiplying by 1
, Double angle formulas - CORRECT ANSWER -cos2x=cos^2x-sin^2x
Cos2x=2cos^2x-1
Cos2x=1-2sin^2x
Sin2x=2sinxcosx
Integral tanx dx - CORRECT ANSWER --ln |cosx| + c ( also the same as ln |secx| )
Integral secx dx - CORRECT ANSWER -ln|secx + tanx| + C
Integral cotx dx - CORRECT ANSWER -ln|sinx|+c
Integral cscx dx - CORRECT ANSWER --ln|cscx+cotx|+c
Power reducing formula; sin - CORRECT ANSWER -sin2 (u) = (1 - cos (2u)) / 2; minus cause
different
Power reducing formula; cos - CORRECT ANSWER -cos2 (u) = (1 + cos (2u)) / 2; plus cause
more of itself
Odd trig integrals - CORRECT ANSWER -best to take out a power and sub from there
Even trig integrals - CORRECT ANSWER -power reducing and half angle formulas are best
Sin and cos trig integral strategy wrap up; both even: - CORRECT ANSWER -power reduce
until you get to the first power
Solutions (Verified Solutions) 2026
Integration by parts formula - CORRECT ANSWER -∫ udv = uv − ∫ vdu
When to use integration by parts - CORRECT ANSWER -when there are two distinct function
multiplied together
LIPET - CORRECT ANSWER -rule of thumb for choosing u; logs, inverse trig, polynomials,
exponential, and trig
What happens if you perform integration by parts and are left with another product - CORRECT
ANSWER -do it again
What to do if you perform integration by parts multiple times, but end up with the same thing as
your og function - CORRECT ANSWER -make this "y" and solve for it
Helpful int by parts tip - CORRECT ANSWER -a possible route is making the entire function u,
and dv dx. Mainly intended to set up easier u sub
Necessary trig identities - CORRECT ANSWER -sin2(t) + cos2(t) = 1
Tan2(t) + 1 = sec2(t)
1 + cot2(t) = csc2(t)
Integral of e^2x dx - CORRECT ANSWER -1/2e^2x + C; reciprocal of coefficient
Derivative of e^2x - CORRECT ANSWER -2e^2x
Simple strategies for trig integrals - CORRECT ANSWER -substitution and multiplying by 1
, Double angle formulas - CORRECT ANSWER -cos2x=cos^2x-sin^2x
Cos2x=2cos^2x-1
Cos2x=1-2sin^2x
Sin2x=2sinxcosx
Integral tanx dx - CORRECT ANSWER --ln |cosx| + c ( also the same as ln |secx| )
Integral secx dx - CORRECT ANSWER -ln|secx + tanx| + C
Integral cotx dx - CORRECT ANSWER -ln|sinx|+c
Integral cscx dx - CORRECT ANSWER --ln|cscx+cotx|+c
Power reducing formula; sin - CORRECT ANSWER -sin2 (u) = (1 - cos (2u)) / 2; minus cause
different
Power reducing formula; cos - CORRECT ANSWER -cos2 (u) = (1 + cos (2u)) / 2; plus cause
more of itself
Odd trig integrals - CORRECT ANSWER -best to take out a power and sub from there
Even trig integrals - CORRECT ANSWER -power reducing and half angle formulas are best
Sin and cos trig integral strategy wrap up; both even: - CORRECT ANSWER -power reduce
until you get to the first power
