Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use C for the constant of integration. 2(x* – x5) dx (6x5 – 5x6)7

Q: 3lnx – 3lny The function f (x,y): x-y Nonhomogeneous Homogeneous of degree 2 c) Homogeneous of degre...

A: The given function is: f(x,y)=3ln x-3ln yx-y          =3(ln x-ln y)x-y          =3 lnxyx-y

Q: ;2 – x + 1 -dx . Evaluate:

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Q: '+ 1 dx 2x e (А A -e-2*) + C B +x +C 4 2 5x +x +C e3 (D) 3 +C e*

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Q: Evaluate: | tan(4x + 3)dx i -In |cos (4x+3)|+C A COS 4 В 4 - In |sin (4x + 3)|+C In |csc (4x+3)|+C D...

A: Given: ∫tan(4x+3)dx =∫sin(4x+3)cos(4x+3)dx Substitute : cos(4x+3)=td(cos(4x+3))=-4sin(4x+3)dx=dtdx=-...

Q: sin(t) Find the equation of the tangent line to f(t) = 9 +9 cos(t) at t = 3 (Use symbolic notation a...

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Q: Which of the following indefinite integrals will result to logarithmic expression? 2 A dx (2x+7)2 B ...

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Q: Vx + sin/x dx. Evaluate: None of the given choices в x- 2cos/x +C 2x+ cos/x + C D x+2cos/x +C 2x- co...

A: Let's find. 

Q: 3. =メー1 x+1 デー

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Q: Vミ-2 lim ミー→4 -4

A: Let, L=limz→ 4z-2z-4Rationalize Numerator L=limz→ 4z-2z-4z+2z+2 L=limz→ 4z-4(z-4)(z+2)L=limz→ 41(z+2...

Q: Which of the following indefinite integrals willresult to logarithmic expre. • Inx. A Ssec-(3x) dx 2...

A: We will find the solution. 

Q: tan3x)dx tan Evaluate: cos23x A - In|sec (tan3x)|+C - In|cos (tan3x)| +C B © In cos(tan3x)| +C in se...

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Q: Let {an} be a sequence of non-negative numbers. Suppose that the sequence {a,} converges to 0. Show ...

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Q: Ni dr A +1 B 2 C) D E) None

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Q: Classify the differential equation: h_p +sec x V dæ4 O Fourth order, third degree, linear ordinary d...

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Q: Radium decomposes at a rate proportional to the amount present at any instant. If initially there w...

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Q: A body moves on a coordinate line such that it has a position s= f(t) = ? - 7t + 6 on the interval 0...

A: Given , S =f(t)=t2-7t+6 and interval 0≤t≤6 Formula: Average velocity =[ f(b)-f(a)]/(b-a)

Q: 1 2х

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Q: patient is adminstered a dose of 60 mg of a drug. If the body naturally disposes of 7​% of the dru...

A: Given query is to find the rate of change after 6 hours.

Q: 19. e* +e = e**y

A: Solution ) ex + ey = ex + y  Differentiate with respect to x d/dx ( ex + ey )  = d/dx ( ex + y ) [ f...

Q: The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres), an...

A: Explained below 

Q: Solve the following (i) |10 - 3x |  ≤ 17  (ii) x² - 6x ≥ 13

A: We have to solve the inequality

Q: Evaluate: Sv*+sin/x dx. A x+2cos/x+ C 2x+ cosx B + C 2

A: We have to solve the integral

Q: Which of the following indefinite integrals will result to logarithmic expression? O Stan(sinx)cosx ...

A: topic - integration

Q: Which of the following integration expression can't be transformed into integral of power Ju"du). @ ...

A: In this question , we can check which integral transformed into ∫un du.

Q: - ydx + (x++ xy )dy = 0

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Q: correct. Canvas uses right minus wrong scheme in che Question 1 IP 15x³ 3x°t is a xp (Choose all app...

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Q: Match the function on the left to its appropriate antiderivative on the right. Prompts Submitted Ans...

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Q: Find and classify the critical points of the function f(x,y)=y^3 +3xy−x^3

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Q: x-e -2r -dx x²+e-2« *2(x-e-2«) A x²+e-2r xp- – 2(x-e-2x) dx x2+e-2r B -2x 2+e =21 dx x²+e-2¢ /2(x?+e...

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Q: A steady wind blows a kite due west. The kite's height above ground from horizontal position x = 0 t...

A: We want to find the distance travelled by the kite. 

Q: S. 9+eoscsiっ.、 (メ)) >マ

A: y = ∫dv4+ecossin-1xTo find appropriate 'dv' so that, anti-derivative is possible.  

Q: The population of Amoeba Proteus is known to grow at a rate proportional to the amount present in a ...

A: Given problem:- The population of Amoeba Proteus is known to grow at a rate proportional to the amou...

Q: (x )dv, using simple substitution dv=f(x)dx_ Determine the value of f(x) if To evaluate the integral...

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Q: tan ( tan3x) dx Evaluate: cos?3x

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Q: Cost C(q) = 86 + 0.13q - 0.007q2 + 0.0009q3. (a) Find C'(100). Interpret C'(100). O This is the rate...

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Q: In order to evaluate the integral expression sin using simple substitution, dv =f (x)dx_ Determine t...

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Q: Which of the following is equivalent to / Isin(Inx?)]²dx , sin(Inx 14) dx A sin2(Inx 14) dx O (sin (...

A: Given that, The given integration is following, I=∫[sin(lnx7)]2dxx We have to find the equivalent of...

Q: Evaluate the integral

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Q: dw 4 Which of the following characterizes the differential equation +v= 0? A 2nd order, 4th degree O...

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Q: +. A 2. B. E) None

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Q: value of c in the equation: dV/dt = -500 (t+1)-2, when  V=700and t=0 is

A: follow next step

Q: C -dx(use 2 decimal places, no 5+x Let * = 2.06, and y = 1.32. Determine the value of when you evalu...

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Q: I. Evaluate the integral of xy dx from x 0 to x 6 using the parametric equation x = 6 cos 0 and y 2 ...

A: Now we have to find the value of integral: ∫06 xy dx

Q: " , [sin(Inx?)]²dx Which of the following is equivalent to sin(Inx 14) dx sin2( Inx 14) dx B © [sin°...

A: The given integral,       ∫sinlnx72dxx

Q: - [Mesin(2x) dx = esin(2x) + C_then the Mis equal to +C,t

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Q: sin³ydy 1+cosy

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Q: dv 4+ ecos(sin-w)

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Q: (x +2x+3)(5-x) 10. g(x)= 3x+2

A: We will use u/v formula for derivative to find the required result.

Q: VI. Show that ydx = y dx it must be (a <h<b)if f(x) = 2x, a = 1, h 2 and b %3D = 4 20. f(x)dx is equ...

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Q: Question 19 Evaluate: / (secx - tanx)-dx A none of the given choic B 2secx - 2tanx -x+C © 2secx - 2t...

A: Given: ∫secx-tanx2dx