Using the substitution u = sin (x), or otherwise, find the exact value of %3D J sin° (x) cos (x) dx. Number

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A: Topic = Integration

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A: Since you have asked multiple questions in a single request we would be answering only the first…

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A: Given query is to find the derivative of the expression.

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A: Here we have to find line integral.

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A: We need to evaluate the following line integral ∫C-ydx+xdy Where,  C: y2 = 6x  from 6, 6 to 0, 0

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Q: Use the Product and Quotient Rules as necessary to find the derivative of f(x) = 7x? cos(x) (Use…

A: The given function,      fx=7x2cosx

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A: The given functions,fu=u8+ug(x)=cos(x)

Q: 25. dx is 1 (B) (©) ! (A) 2e (D) (E) divergent

A: see below the answer and calculation

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Q: A spring has a natural length of 22in. A force of 16001b stretches the spring to 32 in. How far…

A: We will use rules of spring stretch to solve it.

Q: Find V· (V × F), if F(x, y, z) = e*²i+3xe'j – 7e*k. V . (V × F) = x z evz 三

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Q: Edit Evaluate the line integral -ydx + xdy along the curve C : y = 21x from (21, 21) to (0,0). NOTE:…

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Q: 34 Count lim (1+x) F b) lim (1-x)* メ→0 The limit in (a) determines e. What special number does the…

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Q: ||r'(t) x r"(t)|| Use the formula k(t) : to find k(t). 3 r(t) = ei+etj K(t)

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Q: Find the length of the curve r (t) = i + 6t°j + 2t°k, 0 <t < V1 L =

A: We will find the length of curve.

Q: 27. | (u + 2)(u - 3) du 2+x 29.

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Q: A particle is moving with the given data. Find the position of the particle. a(t) = t - 8, s(0) = 4,…

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Q: Evaluate the definite integral. 9ti +3t'j + Vtk) dt

A: The given integral,          ∫-119t i+3t3 j+t3kdt

Q: ,2 COS cos n Σ n3 n=1

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Q: d y Find dx? for the parametric equation: x = et;y3Dt³ +t+1

A: Find your answer below

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 5…

A: To evaluate: ∮C5y2dx+5x2dy Let, L=5y2&amp; M=5x2⇒∂L∂y=10y, ∂M∂x=10x

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A: Given query is to find the limit of the expression.

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Q: Sketch the region R of integration and switch the order of integration. P(x, y) dy dx F(x, y) dy dx…

A: Given: I=∫-22∫x24fx,ydydx The region bounded by the curves y=x2, y=4 from x=-2 to x=2 is shown…

Q: y 3.0아 (1, e) 2.5 2.0아 y-e* 1.5 1.0 y = xe*2 0.5 -1.0 -0.5 0.5 1.0 1.5 2.0

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Q: Evaluate the limit: r(t + h) – r(t) lim h >0 for r(t) = (t°, sint, 1) h r'(t) = (

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Q: Solve the system of differential equations. [ 3 x' 0 - 4. x1(0) = – 12, x2(0) = – 10 - æ1(t) = %3D…

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Q: Find V × (V × F) if F(x, y, z) = 9xyj+2xyz k. V x (V × F)

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Q: Find V x (V x F) if F(x, y, z) = 4.xyj+ xyz k. V x (V × F) =

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Q: Sketch a single graph of a function f(x) which satisfies all of the following the limits and values.…

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Q: Calculate the (f(g(x)))' and (g(f(x)))' derivatives if f(x) = x8 1 g(x) 5x + 1 (Express numbers in…

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Q: Evaluate the indefinite integral: .3 dx x² – 2x + 5

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Q: Find V. (V × F), if F(x, y, z) = 5e"*i+ 6xe®j– 2ek. V · (V × F)

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Q: Find lim f(x) for the given piecewise function. x-4 2х + 5 if x 4 If the limit does not exist,…

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Q: ||r'(t) x r' r"(t)|| Use the formula k(t) to find k(t). 3 ||r(t)||* r(t) = t'i+ t5j K(t) =

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