wow! my.mun.ca X will A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube % Maps Translate Webassign Trick to avoid using simple subs for integrals with (kx + a) rather than x, like ] (2x-1) dx . Q.#1 Please evaluate the following integrals using the (kx + a) trick. Final Answer a) (7-2x)" dx Final Answer b) JV Ty - 5 dy Final Answer c) tan ( 20 ) de5wash my.mun.ca X wil A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube Maps Translate Webassign Final Answer a) J(e-cos(1-0)) de Final Answer dt e) 4t +125wash my.mun.ca X while A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube Maps Translate Webassign TOPIC 2-1(a): Methods of Simple Substitution - Basic Subs Q.#2: Please evaluate sin (7 -2x) dx in following ways. Final Answer a) Using the ( mx + b ) trick for linear subs Final Answer b) Using a full simple sub (i.e. rewriting in u)5wash my.mun.ca X wil A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube % Maps Translate Webassign c) Please state briefly if solutions to (a) & (b) are the same or different, and why. Final Answer Q.#3 Please evaluate the following integrals using full simple sub (i.e. rewriting in u) For these questions, you are given substitution ("u") to help learn s-subs. Final Answer a ) [ti +1 at , u=12 + 15wash my.mun.ca X with A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube Maps Translate Webassign Q.#3 Please evaluate the following integrals using full simple sub (i.e. rewriting in u) For these questions, you are given substitution ("u") to help learn s-subs. Final Answer a ) [tv12 +1 dt , u= 12 + 1 Final Answer +3 b ) (414 ) 11 dt , u=4-145wash my.mun.ca X wil A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube Maps Translate Webassign Final Answer c) [sec x tan x dx , u = tan x Q.#4 Please evaluate the following integrals using full simple sub (i.e. rewriting in u) For these questions, you choose the "u" for the substitution. Final Answer 5x* + 2x a ) dx (x' + x2 ) 135wash my.mun.ca X will A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube Maps Translate Webassign Final Answer cos 2x b ) dx (1 + sin 2x)2 Final Answer dx c) xIn x5wash my.mun.ca X wil A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube Maps Translate Webassign Final Answer d) cosx cos(sin x) dx Final Answer 2x- + x e ) dx (4x3 + 3x2 ) 25wash my.mun.ca X wil A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube Maps Translate Webassign Final Answer dx x (In x ) 2 Final Answer 3x+1 g 9-2x-312 dx5was my.mun.ca X will A2_Written Assignment_MATH X + online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update -> C Gmail YouTube Maps Translate Webassign Final Answer dx h ) (4x -1) In (8x -2) Final Answer In(In x) i) dx x In x3was my.mun.ca X will A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube Maps Translate Webassign TOPIC 2-1(b): Methods of Simple Substitution - Extra Substitution & Similar Special Integrals Extra Substitution Usually helps to factor first to create du/dx & extra term individually, as shown in Q.# 5(a). Q.#5 Please evaluate these integrals: Final Answer a ) [x3 1+x2 dx Initially factor to create dudx & extra term individually [ x' Vitz dx = [x x vitx dx = [ x V1+x x dx EXTRA du / dx Now, proceed with s-sub. Final Answer b ) dx x'+15wash my.mun.ca X with A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube Maps Translate Webassign Final Answer c) [( x3 + 1) 4 x5 dx5wash my.mun.ca X wil A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube Maps Translate Webassign Splitting Up Integral First Q.#6 Please evaluate these integrals: Final Answer a) - 2-x V 1 - x 2 dx Final Answer - er b) dxwow my.mun.ca X will A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube % Maps Translate Webassign Fixing Denominator Choose u so that denominator just u or u " as shown in Q# 7(a), (b), then expand or split up. Q#7: Please evaluate these integrals: Final Answer a) 2t dt u = t + 1 , du = dt t+1 t=u- 1 Final Answer b ) dx u = 1 - x , - du = dx 1 - x x = 1 - u5wash my.mun.ca X wil A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube % Maps Translate Webassign Final Answer X C) dx (8x + 5)33was my.mun.ca X with A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube Maps Translate Webassign Fixing Square Roots, Other Fractional Powers (e.g. )-=(-)1/3) or Other Powers Choose u = inside of root or bracket as shown in Q.# 8(a), change any roots to powers & then expand. Q.#8 Please evaluate the following integrals. Final Answer a) [x 1-4x dx u= 1 -4x du/ (-4) = dx x = (1-u) /4 = 1 1-u 1/2 du 4 4 IJ (1-u) ull2 du , now expand ! Final Answer b ) [ x ( 3 x + 8 ) " dx3was my.mun.ca X will A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube Maps Translate Webassign TOPIC 2-2: Simple Subs for Definite Integrals - later in course TOPIC 2-3(a): Substitution with Inverse Trig F(x)s Q.#9 Please evaluate the following integrals. Final Answer (arctan x)2 a) dx 1+ x2 Final Answer In(arcsin x) b ) dx (arcsin x) V1-x25wash my.mun.ca X will A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube Maps Translate Webassign X C ) dx 1 4 Final Answer 2 d) dx 19 - x25wash my.mun.ca X wil A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube % Maps Translate Webassign 5 e) dx 25 + 16x Final Answer 2 x2 -2x+5 dx Hint: First, complete the square in denominator !3was my.mun.ca X with A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube Maps Translate Webassign TOPIC 2-3(b): Substitution with Exponential F(x)s Q.# 10 Please evaluate the following integrals. You are free to use linear trick where applies if desired. Final Answer a) (8x-4e(5-2x) ) dx Final Answer b) sec2 x etanx dx5wow my.mun.ca X with A2_Written Assignment_MATH X + -> C online.mun.ca/d21/le/content/526584/viewContent/4748726/View Update Gmail YouTube % Maps Translate "Webassign Final Answer c) Je've+l at Final Answer d) ex + 2 ex dx