EXAM 2 MATH 2414 QUESTIONS AND
ANSWERS
integration by parts formula - ans-∫ udv = uv − ∫ vdu sw sw sw sw sw sw sw sw sw sw sw
when to use integration by parts - ans-
sw sw sw sw sw sw sw
when there are two distinct function multiplied together
sw sw sw sw sw sw sw
LIPET - ans- sw sw
rule of thumb for choosing u; logs, inverse trig, polynomials, exponential, and trig
sw sw sw sw sw sw sw sw sw sw sw sw
what happens if you perform integration by parts and are left with another product - ans-
sw sw sw sw sw sw sw sw sw sw sw sw sw sw sw
do it again sw sw
what to do if you perform integration by parts multiple times, but end up with the same thin
sw sw sw sw sw sw sw sw sw sw sw sw sw sw sw sw sw
g as your og function - ans-make this "y" and solve for it
sw sw sw sw sw sw sw sw sw sw sw sw
helpful int by parts tip - ans- sw sw sw sw sw sw
a possible route is making the entire function u, and dv dx. mainly intended to set up easier
sw sw sw sw sw sw sw sw sw sw sw sw sw sw sw sw sw
u sub
sw sw
necessary trig identities - ans-sin2(t) + cos2(t) = 1 sw sw sw sw sw sw sw sw
tan2(t) + 1 = sec2(t) sw sw sw sw
1 + cot2(t) = csc2(t)
sw sw sw sw
integral of e^2x dx - ans-1/2e^2x + C; reciprocal of coefficient
sw sw sw sw sw sw sw sw sw sw
derivative of e^2x - ans-2e^2x sw sw sw sw
simple strategies for trig integrals - ans-substitution and multiplying by 1
sw sw sw sw sw sw sw sw sw sw
double angle formulas - ans-cos2x=cos^2x-sin^2x
sw sw sw sw
cos2x=2cos^2x-1
cos2x=1-2sin^2x
sin2x=2sinxcosx
integral tanx dx - ans--ln |cosx| + c ( also the same as ln |secx| )
sw sw sw sw sw sw sw sw sw sw sw sw sw sw sw
integral secx dx - ans-ln|secx + tanx| + C sw sw sw sw sw sw sw sw
integral cotx dx - ans-ln|sinx|+c sw sw sw sw
integral cscx dx - ans--ln|cscx+cotx|+c sw sw sw sw
ANSWERS
integration by parts formula - ans-∫ udv = uv − ∫ vdu sw sw sw sw sw sw sw sw sw sw sw
when to use integration by parts - ans-
sw sw sw sw sw sw sw
when there are two distinct function multiplied together
sw sw sw sw sw sw sw
LIPET - ans- sw sw
rule of thumb for choosing u; logs, inverse trig, polynomials, exponential, and trig
sw sw sw sw sw sw sw sw sw sw sw sw
what happens if you perform integration by parts and are left with another product - ans-
sw sw sw sw sw sw sw sw sw sw sw sw sw sw sw
do it again sw sw
what to do if you perform integration by parts multiple times, but end up with the same thin
sw sw sw sw sw sw sw sw sw sw sw sw sw sw sw sw sw
g as your og function - ans-make this "y" and solve for it
sw sw sw sw sw sw sw sw sw sw sw sw
helpful int by parts tip - ans- sw sw sw sw sw sw
a possible route is making the entire function u, and dv dx. mainly intended to set up easier
sw sw sw sw sw sw sw sw sw sw sw sw sw sw sw sw sw
u sub
sw sw
necessary trig identities - ans-sin2(t) + cos2(t) = 1 sw sw sw sw sw sw sw sw
tan2(t) + 1 = sec2(t) sw sw sw sw
1 + cot2(t) = csc2(t)
sw sw sw sw
integral of e^2x dx - ans-1/2e^2x + C; reciprocal of coefficient
sw sw sw sw sw sw sw sw sw sw
derivative of e^2x - ans-2e^2x sw sw sw sw
simple strategies for trig integrals - ans-substitution and multiplying by 1
sw sw sw sw sw sw sw sw sw sw
double angle formulas - ans-cos2x=cos^2x-sin^2x
sw sw sw sw
cos2x=2cos^2x-1
cos2x=1-2sin^2x
sin2x=2sinxcosx
integral tanx dx - ans--ln |cosx| + c ( also the same as ln |secx| )
sw sw sw sw sw sw sw sw sw sw sw sw sw sw sw
integral secx dx - ans-ln|secx + tanx| + C sw sw sw sw sw sw sw sw
integral cotx dx - ans-ln|sinx|+c sw sw sw sw
integral cscx dx - ans--ln|cscx+cotx|+c sw sw sw sw
