·S- y dy Vy+2 using the substitution (√√y+2-5) (5√√y+2+y+21) +C 0²/(√y+2-5) (5√y+2+y+24) + C ○ ¾ (√y+2-5) (-5√/y+2+y+21)+C Y Find u+5=√y+2

Q: The integral [₁ face 8 dx S can be transformed to which of the following when trigonometric…

A: We have to solve above integral

Q: Find S y dy y+2 using the substitution V +5=√y+2

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Q: ³ SS ²0 Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,6,0), an

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Q: Evaluate √√√x² + y² ds along the curve r(t)=(4 cost)i + (4sint) j+3tk, -27 ≤t≤ 2T. C

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Q: Does y = (x-5)^(2/3) have a point of inflection?  Discuss.

A: The function y=x-523

Q: 22. Calculate the arc length of the graph of (a) y = f(x) = 1⁄2x³ + x-¹ over [1,3]. Hint: (b) y = 1…

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Q: Suppose m and n are constants and 1 1 —sin(m− n)x+ - -sin(m+n)x+C 2 m-n m+n 1 = cos(m− n)x - 1…

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Q: Find the equation of the tangent line to the curvey = √2-4 at the point (5, 1). Oy=2-1 Oy= 22-2 Ov=z…

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Q: For O x 1/2 -dx and using the substitution=x1/2, the resulting integral takes the form: -du du -du…

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Q: The cost (in dollars) of producing a units of a certain commodity is C(z) = 7000 + 18z +0.5x². (a)…

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Q: ate sin (Inx) dx Integration by parts will be used repeatedly. What is the expression after the…

A: We have to evaluate integral

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Q: What is the value of f(1)- 168 in fx³ Inx dx = f(x) ((1/4) Inx-B) + C? A) 3 B 0 1 2

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Q: For the following problems, find the general solution. 128. y" cos(x) + 2y + y

A: To find the general solution of the following differential equation.y''=cosx+2y'+y

Q: (c) y = 1, y = 1/2, x = 2 (d) y = √x, y = 22, x=9 (e) x = 2y², x = 4 + y² (f) x = 1 - y², x = y² – 1…

A: The area between any two curves is given by formula A = ∫ [f(x) - g(x)] dx  with limits from a to b…

Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

A: The objective is to find the slope and equation of tangent line.

Q: 3. Evaluate the following integral by using the polar coordinates. £²₁, [x²=²²* (x² + y²)³¹ dy dx.

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Q: Suppose that f(x) = 24-223+2-3. Starting with 1 = 2 and using Newton's method, what is the second…

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Q: dx can be transformed to which of the following when trigonometric substitution is used? (x²+4)²…

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Q: find the inverse Laplace Transform of the functions     a.) 5/3s b.)14/((3s+2)(s-4))

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Q: Question Find the area A of the region that is bounded between the curve f(x) = ex-2-3 and the line…

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Q: Let f: CD be a function, with C being the domain and D being the codomain. Show that for any C₁, C2…

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Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

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Q: If f is continuous on [0, 1], prove that f₁¹ f(x) dx = f₁¹ ƒ(1 − x)dx.

A: This question can be solved using properties of definite integrals.

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Q: QUESTION 7 ·S sin²t sin²0 de csc³0 de sec ³0 de cos²0 de The integral dx (x²+4)² 01 Secto 0 + can be…

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Q: 3x5 3x4+6x³3x² - 6x B с + + x + 1 x+m Consider S А Sx √x-m+A x-m+ 14/3 17/6 6 5 -dx. Using the…

A: solution

Q: Consider ∫ x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)?

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Q: Evaluate A B Ⓒ D S= x² - 4x 2 x² - 4x 2 x2-2x 2 x²-2x-In 3x5 3x4+6x³3x² - 6x - (x-1) 1/6(x+2) 16/3…

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Q: ormulas to compute the following antiderivative. x-1 x² -dx.

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Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

A:

Q: Compute the left and right Riemann sums L4 and R4, respectively for f(x) = √4x² on [-2, 2] and…

A: We can find Left and Right Riemann sums .

Q: Solve the following differential equations: 2 √1-y² (a) - dx + y sin 2x -dy = 0 cos 4x+1

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Q: Evaluate tan" (x) sec¹x dx m+ 1 m+1 1 m+2 B D -tan (m + 1)(x)-tan (-1)(x) + C m - 1 (m+1)(x) +tan…

A:

Q: 18. A radioactive substance decays exponentially: The mass at time is m (t) = m (0) ekt, where m(0)…

A: Concept: Mean life of a radioactive substance: The average life of all of the nuclei of a positive…

Q: For the function f(x) = 2x4 - 16x2 , find and identify any extrema (maximum/minimum) using the…

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Q: The integral S³ S S Sse x dx x²+√√x²-1-1 sece tane de sece - 1 cose d 1 - sino sine de 1 + cose…

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Q: Question 9 The integral - dx (x²+4)² can be transformed to which of the following when trigonometric…

A: The given  integral can be transformed to which of the following when trigonometric substitution…

Q: Suppose the revenue from producing (and selling) x units of a product is given by R(x) = 8x-.01x²…

A: Marginal revenue at (x=30) =dRdxx=30

Q: Suppose m and n are constants and m #n. Evaluate sin(mx) cos(nx) dx 1 Ⓒ[con(-)x-cos(m + n)x] + C B −…

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Q: The rose r = 3 cos (50) is shown below: 3 -3 Find the area of the region bounded by one loop of the…

A: We need to find area.

Q: remaining

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Q: dx (x²+4)² The integral A÷/csc²³ Ⓒ + /sec²0 B C Ⓒ + / sin² D 8 csc ³0 de c³0 de cos²0 de sin ²0 de…

A:

Q: 9. y(y² + 1)dx + x(y²-1)dy = 0 Ans: + xy = c

A: We  are given the differential equation to be solved    =>       y(y² + 1)dx + x(y²-1)dy = 0

Q: Find Vector A and B such that A is parallel to , B is perpendicular to and A + B = if you already…

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Q: y dy Vy+2 (√3+2-5) (5√3+2+7+21)+C (√3+2-5) (5√3+2-1+24) +C 3 Ⓒ(√3+2-5) (5√3+2+3y+24)+C…

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

Q: 1 3 Find the area bounded by the curve y== -x3. -x² + 3x and the line y=x. 16 10 square units 8…

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Q: Let integral in the order of dadzdy, then what are the limits of integrations? A.0 sz55, Osys…

A: Concept: Changing the limits of the triple integral: A sequential triple integral can be presented…

Q: In an autocatalytic chemical reaction, the product form is a catalyst for the reaction. If Qo is the…

A: SOLUTION-

Q: Question 4 Evaluate sin (Inx) dx- Integration by parts will be used repeatedly. What is the…

A: