When applying the variable change u-cosy in the in the following integral: [ f(cos y) sen³y dy What option is equivalent to the integral shown: Oa) f(u)(u² - 1) du Ob) [ f(u)(1 − u²) du Oc) [f(u)(1-³) du Od) ff(u)(u³ - 1) du

Q: quickly

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Q: The chain rule of antiderivative is stated as: ff (g' (x)) g(x) dx = F (g(x)) + C True O False

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Q: The function f(x), which is defined for a ≤ x ≤ b, has the following behavior: f'(x) 0. Choose the…

A: Follow the procedure given below.

Q: II. Evaluate the following integrals. 1. 1 - coth² (log₂x) x cosh (log₂ x) -dx

A: The integration of the integral is;  [1-coth2(log2x) ]/[x cosh(log2x) ].

Q: 1. Solve the differential equation of order one. Show your solutions. y' = x - 2y STEPS: a. Put…

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Q: Given that R' (t) = 2ti — 2j + 3t² k and R(2) = i + j — k, then R(t) =

A: The objective is to find R(t).

Q: The following differential equation is a Bernoulli equation: 2 dy + 27/ y3 where y = f(t) dt By…

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Q: So x² (a²-x²) ³¹/2² dx

A: A detailed solution is given below.

Q: answer a and b a. The marginal cost of manufacturing x tarpaulins is given by 0.03x2 + 0.4x + 7. If…

A: Explanation of the answer is as follows

Q: Find the equation of the line tangent to y = e The equation of the line tangent is y= at x = 1 - In…

A: Given query is to find the equation of the tangent.

Q: Calculate the amount of money Cynthia had to deposit in an investment fund growing at an interest…

A: To find out the amount of money that Cynthia has to deposit.

Q: 14. Find a function whose tangent has slope 4x+1 for each value of x and whose graph passes through…

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Q: 3 foa 0 (|3x − 1| + |3* – 3|) dx

A: Use integral concept

Q: Perform the following integration. 1. (sinhæ)(coth? a+csch® a) dự sec³ x tan x 2. S dx √2 + sec x 3.…

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Q: lim (tanx) (sin x-1) x→ 17/1272 π +

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Q: The tenth term of an arithmetic sequence is 23, and the second term is. Find the first term. X

A: Let's find first term of arithmetic sequence.  Tenth term = 73/2 Second term = 9/2

Q: Can you solve this and show work clearly, the first part is X to the 3

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Q: Evaluate the limit using the L'Hopital's Rule 1 - cosh x lim x+0+ ln(x² + 1)

A: SOLUTION-

Q: 4. Swin (w - 2) dw

A: The given integral is: I=∫wlnw-2dw   Apply the integration by parts to solve the above integral.…

Q: Answer

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Q: Find the surface area generated b rotating the portion of the parabolic arc x = y^2 from x = 0 and x…

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Q: Find the area bounded by y = 2 - x² and y=x a. 9/2 b. 7/2 C. 5/2 d. 3/2 e. NONE OF THE ABOVE

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: y = coux, X = Find the are a OF i) sketch the area. ii) Determine the boundarier by ) Set-up the…

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Q: The following differential equation is a Bernoulli equation: 2 dy + y3 where y = f(t) dt t By making…

A: Using substitution Z=y^n, and n=1/3 We get the linear differential equation

Q: Is that pi (π)? Or something?

A: Given ,  Area of the region bounded by  y = cosx , x = -π/2 and x = π/2 and the x - axis  We have to…

Q: fsec³ 7x tan5 7x dx 4.

A: Let's solve given integration.

Q: 7. A particle moves along the x-axis with its velocity modeled by the function (t)= 3cost + 3t. The…

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Q: Find the volume of the colld_generated by. revolving the area bounded by the given curves_ about the…

A: We need to find volume.

Q: The choice of u and du is subject to trial and error. Identify the appropriate choice of u and du…

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Q: A.The table indicates that a(1)= 2m/s. What does that tell you about the velocity B. The table…

A: Given

Q: Use the First Derivative Test to find any relative extrema of the function. (a) g(x) = 2x³ – 18x

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Q: What is the center of gravity of the solid formed when the plane region bounded by 2x + y -2= 0, y =…

A: The given region is as follows: Now, rotation of the bounded region about y-axis will result in a…

Q: 1. Why is it important to use the six trigonometric ratios in getting a missing angle value?

A: The six trigonometric ratios are sine, cosine, tangent, cotangent, secant, and cosecant. Basically,…

Q: True

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Q: X(jw) = 8.8cos (3w) sin(0.5w)

A: Given function is:X(j,w)=8.8cos(3w)sin(0.5w)we have to find the value of X(3,5).value of…

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: The solid generated by x+y=5, y=0 and x=0, about y=0

Q: -2 S₁² S₁² (²x²y^² + 2 (2x²y-² + 2y) dy dx 1 1

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Q: 3. S x² ln xdx

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Q: Let f(x,y) = 8x - 2y + 5. Find the following values of f(x,y) for the given coordinates. (a) f(2,…

A: Given  f(x,y)=8x-2y+5 Find:f(2,-1) Substituting x=2 and y=-1 in the given equation, we get  f(2,…

Q: Test for exactness then solve. (1 +  y2)dx + (x2y + y)dy = 0

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Q: Find the value of t 20 + 10t - 4.905€ ² =0

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Q: Determine the order of the given differential equation and state whether the equation is linear or…

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Q: A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t²…

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Q: Evaluate fsin² 2xdx Show step-by-step solution.

A: We need to do integration of  sin2(2x)  First we will apply it's formula, since this value is equal…

Q: Given two functions F and G, we say that F is an antiderivative of G when O F'(x) = G(x) for all a…

A: Above two questions are answered.

Q: Find the grea i) Sketch the ii) Determine the iii) vet up iv) Integrate 7) y=vin of the boundaries a…

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Q: Electric usage over the course of a day varies. The graph shown is of electricity costs per hour.…

A: Use average concept

Q: 1 X 4 11-x²

A: Please refer to the image below

Q: Suppose that the number of crates of an agricultural product is given by 11xy-0.0002x² - 5y Z= 0.03x…

A: Suppose that the number of crates of an agricultural product is given by z=11xy-0.0002x2-5y0.03x+4y…