1. Do the integration by substitution for the following integral and find the value of definite integral. 12x 2x2 + 2

Q: find (2n +1)! = 120

A: Here we have to find the value of n.  2n+1!=120

Q: Suppose a product's revenue function is given by R(g) = - 2q? + 400g. Find an expression for the…

A: Given problem:- Suppose a product's revenue function is given by R(q) =- 2q2 + 400q   Find an…

Q: 21 3x7 + 8x 5x

A: Given: y=3x7+8x5-215x

Q: Compute f(x)dx f(x) = { 2x if x <1 4 if x 21

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Q: Find the moment of inertia of the area bounded by the curve x^2=4y, the line y=1 and the y-axis on…

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Q: Find the divergence of the vector field F. F(x, y, 2) = In(7x2+ 6y? )i + 42xyj + In(6y2. + 72² )«…

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Q: 1 Which of the following is an antiderivative of the function f(r) = %3D 5+ x2 (a) 2x In(5+2?) 1 (b)…

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Q: 6. Determine. 2r - 3x 4x SET A.

A: I have stated the used formula in the solution

Q: x2 - 8 R2.1 J x2 + 5x + 6 Answer with text and/or attachments

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Q: įy'ny dy 2e' +1 Ans. 9. 13.

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Q: Sins 느 x Uos

A: We need to evaluate integral.

Q: 2 x – 4 dx .2 1

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Q: on the interval Find the difference between the upper and lower estimates of the distance traveled…

A: Let's find.

Q: 5x2+11x+2 dx x(x+1)²

A: integration using partial fraction

Q: Evaluate the line integral / (2x + 4y)dx + (2x – 9y)dy along the curve C : x = 4 cos t, y = 8 sin t…

A: Solution is given below:

Q: 1+2x2 dx J x2(1+x?)

A: A detailed solution is given below

Q: Find the centroid of the region bounded by y = VI and y = x². U

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Q: Consider three connected lakes, A, B, and C, where lake B has a volume of 2650 km, and water flows…

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Q: [x+1

A: The objective of the question is evaluate the indefinite integral.     Note -  As per our guidelines…

Q: [1 1 1] Suppose we have a matrix A= |1 0 1 2 1 2 What is rank of A?

A: GivenA=111101212R2→R2-R1R3→R3-2R1A~1110-100-10R3→R3-R2A~1110-10000We know that The rank of a matrix…

Q: What is the amplitude of the function y=f(x)= 2sin A) 3 в 5 c) 2 D) 7

A:

Q: (a) / Which of the following integrals is equal to -2+ In 2? X - 4 dx (a) 4- I dx (b) 2 - 4 da (c),…

A: To find which of the given integrals has given value

Q: dy Solye the differential equation 3a2y = = -y, s.t. y (0) :

A: Topic = Differential equation

Q: For the cruciform in the figure below, the equation is x²y2 - 9x2 – 4y2 = 0, find the equation of…

A: To find the equation of the tangent line for the given curve.

Q: Verify Green's Theorem by evaluating both integrals ам y? dx + x2 dy dA ay for the given path. C:…

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Q: Suppose a product's revenue function is given by R(g): is units sold. Also, it's cost function is…

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Q: Verify Green's Theorem by evaluating both integrals aN dA Lv? dx + x² dy = ду ax for the given path.…

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Q: Given the expression below, y = ecos arc sec(ln(r |- determine y.

A: The derivative is given below

Q: Find the area of the region enclosed by y 3.5x and a = 6 – y?. Use horizontal strips to find the…

A: Given

Q: test conerg ence and clivergence h!

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Q: y = (sinh(@)) Solve for y'. Express your answer by factoring out a common facto

A: First I have taken the log on both side to the given function and then differentiating it with…

Q: What is the range of the function y=f(x) =2sin 57 A [-3,7] B B [-7,-3] В © [-7,3] D D [3,7]

A: We have to find range of give function.

Q: Find the dimensions of a rectangle with perimeter 1000 metres so that the area of the rectangle is a…

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Q: x² + 4x + 1 dx (x – 1)(x + 1)(x + 3) d* - Inlx- 1+Inlx+11- n|r+ 3| +C Inlx- 11+Inlx+1| +Inx + 31 +C…

A: Let's find.

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) sin(9t), lim t-0 e5i +…

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Q: |i cos t?dt can best be evaluated by: A Trigonometric Transformation B) None C Integration by Parts…

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Q: Given the following equation, determine y using the methods discussed in class a - y = cosh(cy) |

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Q: sec'xdx

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Q: Problem 4. Explain whether or not the following sets are subspaces of the given vector space +6] -b:…

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Q: 3e dt 10. SET A.

A: We will use the concepts of definite integral

Q: (45)ds。(特)"- sa (49) 48 (xs) 1-1

A: The given integral is (x2+5x) /(x+9)1/4.

Q: Question 1 Which of the following is false? O yofe" = eu . Ine u (x) In e O yof log, u = u' (x) In a…

A: We can solve as follows

Q: 2 and common ratio Write down the first four terms of the geometric sequence with first term (Type…

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Q: d Find [r(t) · u(t)] and [r(t) x u(t)] in two different ways. dt dt r(t) = ti + 2t2j + t³k, u(t) =…

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Q: Evaluate the following sum: 3x + cos 2016 + cos (Write your answer in the simplest form, use…

A: The given sum,1+cosπ3+cos2π3+cos3π3+cos4π3+......+cos2016π3

Q: If y=f(x) = - 3cos+) + 4 then what is the value of / 2 A) 7

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Q: Solve the equation algebraically. Round the result to three decimal places. 3+ln x = 0 8 e-354.598…

A: Using algebra

Q: Given the linear differential equation: y'' - y = cos(x) - 5sin(2x) Find the general solution…

A: Solving

Q: Evaluate the definite integrals. (4 significant figures) cosec-4t dt 9. SET A.

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Q: S(1 – 2x²)(x + 3)dx

A: