Write TRUE or FALSE before each statement. Solve y' - ³y = dependent variable. differential equation. differential equation. Statement 1. The integrating factor is 3. Statement 2. The given differential equation has y as its 4 Statement 3. y = - + ce is the solution to the above Statement 4. 3y = 1 + ce is the solution to the above

Q: HOMOGENOUS LINEAR DIFFERENTIAL EQUATIONS. (D^3 – 2D + 4)y = 0 ; y = –2 , Dy = 8, D^2y = 0, when x =…

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1₁ 1 A -unit² (B) unit² 1 H|m

A: Given that fx=x+13  and gx=x+1Solution :x+13=x+1x+13-x+1=0x+1x+12-1=0x+1=0 and x+12-1=0x=-1 and…

Q: Evaluate the improper integral 3 A 4 B) diverges с 0 D 2 N|O √√² 3³/3 m|f dx

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Q: Evaluate: L-¹{. S-2 (s+ 2)² - 49 4 Â) e-2t(cosh7t - -sinh 7t) 4 B e²t(cosh7t + sinh 7t) (C) e2t…

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Q: Given A B C D f(x) dx = 0 and 11 6 0 ¹² f(x) dx = 11 6 I 11 5 55 6 evaluate S²3f(x) dx - ₁2f(x)dx.…

A: we have to find the integral

Q: In the indefinite Integral Sin(cosh x + ex)- A In(cosh x + e*) B sinh x + ex C In(cosh x + e*)- sinh…

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Q: What is the integral of the shaded region? * 8(y)-f(y)dy A. OA OB Oc OD B. İf(y) - g(y)dy a C. f(x)…

A: To find out the correct answer.

Q: Which of the following is homogenous of smallest degree? (A) In x - In y B x+y x-y C √x-y x² + y4 X…

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Q: Find the volume of the solid of revolution generated when the area described is rotated about the…

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

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Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

A: the line y=x-1and y=(x-1)3 intersect in the points (0,-1),(1,0) and (2,1) the line y=x-1 is below…

Q: The general solution of (D³+4D)y=0 is Ay=e*(c₁cos2x+c₂sin2x) B y=c₁+c₂cos2x+c3sin2x Ⓒy=c₁еx+c₂e²x +…

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Q: e integral be 'solvable' using trigonometric substitution. What is the correct choice of u given J…

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1₁ 3 Ⓒ / unit² A ® B -unit² C…

A: This question can be solved using area bounded by two curves.

Q: . The daily amount of smog produced by cars coming into a city is given by y = 2 + 0.01x3/2, where y…

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Q: Find the area bounded by : f(x)=e*, g(x)=e*, A) (e²-1)² e² sq. units B (e²+ 1)² e² (C) (e³-1)2 e3 D)…

A: In the given problem we have to find out area of region bounded by given curve with the help of…

Q: Which of the following can be determined given .3 3 3 [ f(x)dx = 5, ³g(x) dx = 7, and g(x) dx = 7,…

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Q: Evaluate the integral: e3+cosh2x33+cosh2xsinh2x dx (Α) (3e)3+ sinh2x 2+In3 + C (3e)3+cosh2x B 2+2ln3…

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Q: Which of the following can be determined given f(x)dx=5, g(x)dx=7, and h(x)dx= -5 Ⓒ [²(f(x) + g(x) +…

A: Give∫13 f(x) dx = 5, ∫03g(x)dx=7, and ∫13h(x) dx = -5

Q: d If g(x)=- S* [e²-In (21+1) ]dt, find g(x). -2 2 (2x + 1)2 4 B (2x + 1)² Ⓒe-In(2x+1) 4 (2x + 1)² di…

A: We have to find out derivative

Q: sinh xte cosh x + ndefinite Integral Sin(cosh x + e*)- In(cosh x + e*) sinh x te cosh x + ex

A: We have to calculate the given indefinite integral according to the given information

Q: A tank contains 50-liters of brine in which 20 grams of salt is dissolved. Pure water is being…

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Q: Determine the integral: [x²cosxdx A x²sinx + 2xcosx+2sinx + C B x²sinx + 2xcosx-2sinx + C (C)…

A: Given,∫ x2cosxdx

Q: Initially 73 grams of radioactive substance was present. After 3 hours the mass had decreased by 6%.…

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Q: •+∞0 The improper integral * fe 0 A) 0 B e C (D) 1 ∞ ex dx is

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Q: Question 25 x + 2 Determine the case of the following proper rational function after simplification:…

A: We have to determine proper rational functions and choose correct options

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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Q: y = Arctan ( 2+x 1-2x

A: The derivative are

Q: Transforming dx using miscellaneous substitution will yield to secx + 1

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Q: cylinder cone pyramid if this triangle is rotated about the x axis, what figure is formed?

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Q: The general solution of the equation (D4 +D²)y= -12 is A y=c₁ + c₂x + c3cosx + casinx+3x² B y=c₁ +…

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Q: The function is X 2 = y² What is 8²% მ2 Y x²

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Q: dx Transforming secx + 1 2-2z² A 1+z² ® √ ₁ + 2²/1d² +z² B -dz 1-z² z²+z C / 1-z² Ⓒ / 1-²/²0 D 1+z²…

A: To find the transformation of the integral ∫dxsec x+1 after using miscellaneous substitution.

Q: S dx secx + 1 Transforming Ⓒ / + A -dz 1+z² 2-2z² (B) 1+z² C 12²+2 dz Ⓒ √ 1+2²2 dz D 1-z² -dz using…

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Q: Solve the following y" - 3y' + 2y = 2x2 + ex + 2xex + 4e3x -

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Q: In ( x² + 3x -=-7) dx X-2 Evaluate the integral: Se Ⓒ + A x² 2 =+ + In|3x-6|+C ℗ +² +5x+3n|x-2/+C B…

A: To find out the integration.

Q: Question 33 Evaluate: :S₁ A B с D dx (x+1) log(x+1) -In[log(x+1)] +C In 10 -log² (x + 1) + C 2 -In…

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Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x)=x²+2x+…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and…

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Q: Let g be a differentiable function, and let the range of g be an interval I. Suppose that f is a…

A: If a function F is an antiderivative of the function f then F'(x) = f(x) , and ∫f(x)dx=F(x)+C for…

Q: Given the integral sec6 (x - 1) tan4 (x - 1)dx, which of the following equatio useful for…

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Q: How many antiderivatives does a function of the form f(x)=x" have when n*0₂ A infinitely many B may…

A: We have to choose correct option

Q: Question 12 We can apply General Power Formula of Integration on which of the following integrals? A…

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Q: Given than f(x) dx = 4 and A None of the given choices ℗ 25 (2) dx = [1 (2) de B f(x) © f (x) dx =…

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Q: What kind of the polar graph has the equation r = 2 + 2 cos 0? limacon cardioid lemniscate…

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Q: The improper integral ** ex dx is A Be (C) 1 D) 0 8

A: ∫0+∞e-x dx

Q: Evaluate the triple integral: A) 6 B) 18 C) 24 D) 12 3 2 1 ²³√ [²√ √ 0 (x+y+z)dydxdz

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Q: Determine the general parametric solution of the following unsolved differential equations for the…

A: See the details solution in below

Q: --——-^*[e'-In(2t+1)]dt, find g'(x) . dx 4 A e*+ (2x + 1)² 4 B et + (2x + 1)² 2 (C) e*- - (2x + 1)²…

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Q: (D5+ D4-7D3³ - 11D²8D-12)y = 0

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