Is y=e−3x+x−3 a solution to the initial value problem shown below? y′−3x=−8−3y y(0)=−3 yes or no?

Q: Use the areas shown in the figure to evaluate f(x) dx, y = f(x) Area = 1.5 5 Area = 0.8 a b d Area =…

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Q: Determine the value of C in on the antiderivative of F(x) = sin°(x)cos“(x) for x = 0.108 and y =…

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Q: Which of the following trigonometric substitutions is the most appropriate to the intgral (4e2x +…

A: Given query is to find the most appropriate substitution.

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Q: Which of the following is equal to sec 2x tan³x dx to obtain the correct indefinite integral? A x-…

A: The given integral,        ∫sec32x tan3x dx

Q: Let f(x,y) = C be the antiderivative of F(x) = x²cos(2×), Determine the value of C if x = 64 and y=…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (4x2+ 5x4)dx By method of partial fraction, the integral | - can be evaluated when expressed as…

A: We find out the partial fraction decomposition of given integral. Follow 2nd step.

Q: find the limit

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Q: *xe' de (x+1)2 Using integration by parts to evaluate it is best to let dx A u=xe"; dv =- (x+1)2 x…

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Q: (9x-10) where "a" is f (x) = -i F (x) = 30

A: Follow the procedure given below.

Q: Given G = {a | a EN and 368 < a < 400} %3D G has subsets. G has proper subsets. Add Work

A: This is a problem related to set theory. Based on the general formula we will answer the question.…

Q: de Evaluate: x – a A f(x) = -3 ln (|1 – V|) + C B None of the given choices © f (2) = 3 ln (|1 – V|)…

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Q: Detemine the value OF C IF X=1-co2 and y =1.B9 when you evaeuate Scot"(2x)dx. Cure radiar form Of…

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Q: 25 -x2 In -dx , if we let u =/ 25 – x2 , then udu = - xdx. (А) True B) False

A: We can solve as follows

Q: is (use radian form of angle measure. answer in V1- x2 2 decimal places no space) Add your answer

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Q: Which of the following is true? ® Ssin(3x)cos(4x)ax =S sih(7x)= sin(x) A 2 ® Jsin(4x)cos(3x)ax = […

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Q: Let x = 1.14 and y = 1.58. Determine the value of C when you evaluate cot *(2x)dx.(use radian form…

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Q: Let x = 1.19 and y = 2.02. Determine the value of C when you evaluate cot *(2X)dx.(use radian form…

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Q: Question 15 The x²-4 dx can only be evaluated using trigonometric substitution technique . A True В…

A: Follow next step

Q: /x[cosh?( 2x²) – sinh²(2x²) ]dx is equal to (A) x?dx B) None © Sar dx (D 4 xdx E xdx

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Q: Evaluate:- 4 dx ④ -VR-4-2sec-1(즉)+c A =/x2 – 4 + sec + C (c) =2/x2 - 4 + sec -/R-4+2sec-1(즉)+c x2. +…

A: Integration

Q: 2x +1 The antiderivative of f(x) is (x – 3) (x – 2) A F (x) = 5 ln x – 3 + C x – 3 7 x - 2 B None of…

A: Here we have to find the antiderivative of the given function f(x).

Q: The integral expression J xsin-(2x)dx can be evaluated using integration by parts of the form udv =…

A: This question is based on integral by parts.

Q: То evaluate y?csc?(y³) cor2(y³)dy, we let u =csc(y³) A True B False

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Q: Determine the value of C in on the antiderivative of F(x) = sin (x)cos*(x) for x = 0.067 and y = 1.…

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Q: Which of the following is true? cos (x), cos (x) cos1°(x) O Ssin*(x)cos°(x)dx =- + C 10 A 4 ®…

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Q: © J tane x*dx Using trigonometric substitution technique, the simplified integral after substitution…

A: sec2(x)-1= tan2(x)

Q: Determine the value of C in on the antiderivative of F(x) = sin (x)cos“(x) for x = 0.125 and y =…

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Q: *dx Evaluate: 3x + 4 A None e 3x, ! sec-1 В +C |

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Q: Question 8 Evaluate: Jcos 2xdx cos³2x + cos2x A + C 2 cos³2x + C 6. cos2x B sin2x sin32x + C 6.…

A: topic - integration

Q: A camera is set up at the starting line of a drag race 60 ft from a dragster at the starting line…

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Q: What is f 2sm z cos e sin x dæ? 2sin z +C In 2. 2sin z +C In 2 2cos z +C O A. O B. In 2 20os z +C D.…

A: NOTE-Since you have asked multiple question, we will solve the first question for you. If youwant…

Q: Let f(x,y) = C be the antiderivative of F(x) = x<cos(2x), Determine the value of C if x = 35 and y=…

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Q: dx dx is converted to: 4+Vx By algebraic substitution, the integral - 2ydy y+4 B y+4 © [ vdy y+4 dy…

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Q: In solving for the antiderivative of f(x) = (9 - x2)3/2 using trigonometric substitution, f(x)dx is…

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Q: (x+1) dx If A B C + + dx ,the values of A & C respectively are (x+2) (x- 1)2 (x – 1)2 x+2 X- 1 3

A: We will evaluate the integral using partial fraction as following.

Q: dæ Evaluate: a/9x2 + 4

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Q: To evaluate sin42x cos 2x dx , the identities to be used is/are: sin22x = 1- cos?2x В cos²2x = 1-…

A: Check the identities

Q: xỉ (9x" –10) where "a" is equal to The antiderivative of f (æ) = - is F (x) : 30 (A B 1 6. 1 12 E…

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Q: 1 Which of the following is the antiderivative of f (x) (x + 2) – Va+2 A) None of the given choices…

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Q: (을) Using the miscellaneous substitution z=tan match the integral expression on the left to its…

A: Given problem:- 3.  ∫ dθ/(2-3 sin(θ))    4. ∫ dθ/(3 sin(θ) +4 cos(θ) +5)

Q: To evaluate sin*2x cos 2x dx , the identities to be used is/are: sin4x, 1- cos4x A 2 B cos²2x=1-…

A: Solution:-  This types of trignometric integrals can be solve by reduction formula of integral.

Q: Evaluate: Jy?cos2ydy 글an2y-글ycos2y+ 금snzy+ A 1 1 1 żsin2y-ycos2y-sin2y+C В 4 1 © sin2y+ycos2y+sin2y+…

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Q: Let f(x,y) = C be the antiderivative of F(x) = x-cos(2x), Determine the value of C if x = 6 and y=…

A: This is a problem related to integral. Based on the general formula of integration we will solve the…

Q: A Jsin(3x)cos(4x)dx = [ sin(7x) – sin(x). A dx 2 * cos(x) – cos(7x) ® Ssin(3x)sin(4x)dx= [co c) All…

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Q: sin u n tanmudu, where m is any positive integer, we use the transformation for tan?u= cos?u A True…

A: Follow next step

Q: Determine the value of C in on the antiderivative of F(x) = sin°(x)cos*(x) for x = 0.427 and y =…

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Q: To evaluate | sin42x cos 2xdx conveniently, the formula/identity to be used islare A sin²2x=1–…

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Q: Evaluate each of the following indefinite integrals: Show complete and detailed solutions. Express…

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