To evaluate [x²cosx dx' -2 / COST. 2sinx -2/cosx 2 / COST x2sinx – 2x cost x2sinx+2x cosx − 2 x2sinx + 2x cosx − 2 x2sinx – 2x cosx+2 use integration by parts. What is the expression after the second integration by parts? cosx dx + C sinx dx + C cosx dx + C cosx dx + C

Q: Question 8 x1/2 S dx and using the substitution = x 1/2, the resulting integral takes the form: X-X…

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Q: Exercises To Solve [No.5] 4 S (X-+1) √ X ²2X-3 3-2x-x²

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Q: An arithmetic sequence has the 5th term equal to -64 and the 14th term equal to -1. Calculate the…

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Q: Question 4 What is the value of f(1) - 16B in J x³ Inx dx = f(x) ((1/4) Inx - B) + C? A) O B) 1 (C)…

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Q: S= The integral dx can be transformed to which of the following when trigonometric substitution is…

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Q: Ex: If w cos(uv), u = xyz, y = TT 4(x²+y²)' aw find at point (1, 1, 1). əx

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Q: Let S be the surface with equation (z - 4)² = 4x² + 4y². Viewing S as a surface of revolution, find…

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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: 2. Differentiate the following: a. y = 2x-2y b. 2sinxcosy=1

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Q: Use the quotient rule to find the derivative of the following. 2x-3 y= 7x+5

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Q: dy dx ³-√√3x² 2 √5x

A: We will solve the problem

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: Evaluate S tan" (x) sec¹x dx. I A tan (+1)(x)tan (-1)(x) + C m+l - 1 I B tan (+3)(x) +tan (+1)(x) +…

A: Let's evaluate given integral.

Q: Use Simpson's Rule to evaluate the following. n = 10 +3 1 dx J-3 1+x²

A: SOLUTION-

Q: What is the average rate of change of y with respect to z over the interval [-3,-1] for the function…

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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: Set up, but do not evaluate, the integral to find the area of the surface generated when the curve y…

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Q: What is the approximate value of 24 that is found using the tangent line to at x = 16? Round to the…

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

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

A: We have to find the inner radius

Q: lim F(x) lim F(x) x--6 What is the value of the limit? Select the correct choice below and fill in…

A: We have to find the limit

Q: Consider ·S= x-m+- Sx 3x5 -dx. Using the method of partial fractions, the given integral can be…

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Q: (ii) tank (In x) = x²-1 x² +1

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Q: To integrate by u-substitution, which part of the integrand should you choose as u? S cos de sin² z…

A: We have to find out the substitution

Q: 5. Evaluate the following triple integral. ſſſ (.x² + y² ) dx dy dz D D={(x,y):x² + y² ≤9.15:53)

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Q: Use the slopes of tangents to determine whether the function f(x) = -6x²+36x is increasing,…

A: The given function f(x)=-6x2+36x at the point x=4.

Q: Use Euler's method to solve the following ODES wwwwwwww dy dx = -2y + 4e¯*, with h = 0.18 from x = 0…

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Q: Ji 16 sin² x cos² x dx dx B

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Q: Solve y at x=1. dy/dx - 2(x+1)^3 = 4y/(x+1)

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Q: 2. Determine parametric equations of the line that.... 4 a) passes through (-9,8) with slope - 5 b)…

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Q: Suppose a population of fruit flies changes at a rate of g(t) = -4e0.041, in flies per day. If the…

A: Topic:- application of integration

Q: Differentiate the function: y = e-x cos²x x²+x+1

A: To differentiate the function.

Q: Exercises To Solve [No.5] 05² dx 3dx x²+²x+5 9x²6x+5

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Q: 172. Evaluate the definite integral using the Fundamental Theorem of Calculus, Part 2. 3 La+…

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Q: Find arc length for the curve (y+1)2=4x3 x=0 ,x=1

A: This question can be solved using the concept of length of arc of a given curve over a given…

Q: 7. xdy = (5y + x + 1)dx Ans: y = -x-+cx5

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Q: Evaluate the integral S√x Inx dx 3 2 4 -x² Inx+ x² + C 03x³nx-x²+c 4 2 -x² Inx+ 2 C 15 3 2 4 °²x²nx…

A: We have to solve above integral

Q: need the answer quickl

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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: Find the equation of the tangent line to the curve y = 5x² - 7 at a point x = 1.

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Q: True or False: lim O False O True 2² + 3x - 1 14-2 2-9 3 11

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Q: Question 6 6dx For the method of partial fractions, to evaluate S90 -1 = S Adx + S = X-1 Bdx X+1'…

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Q: For the following exercises, find aj dt and direct substitution. 226. f(x, y) = x¹, x=t, y=t using…

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Q: ·S S For S- x 1/2 -dx and using the substitution=x 1/2, the resulting integral takes the form: 4u…

A: topic - indefinite integral

Q: What is the value of f(1) - 168 in x³ Inx dx = f(x) ((1/4) Inx - B) + C? 02 1 03

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Q: Consider I x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? O 1/4…

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Q: 2. Consider the circle C₁ : r = 1 and the roses C₂: r= cos 20 and C3 : r = 2 cos 20, each of which…

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Q: Show that the three functions: f₁(x) = ex-8,f₂(x) = ex, f(x) = 4(2x-2) are linearly dependent.

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Q: Let T be the tetrahedron with vertices (4, 0, 0), (0, 5, 0), (0, 0, 5) and the origin. Write f(x, y,…

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Q: 1. If x=27-3k and y = i +5j -4k, express each of the following in terms of i, j, k b) 2(3x+y)-3(4y…

A: Given x→=2i→-3k→ & y→=i→+5j→-4k→To write expression in terms of i→,j→,k→:

Q: The polynomial function f is defined by f(x) = −2x² + 3x³ + 5x²-x-5. Use the ALEKS graphing…

A: We need to find local maximum.