Use the Fundamental Theorem of Line Integrals to calculate ∫c F*dr exactly, if F= x^(2/5)i +e^(y/5)j, and C is the quarter of the unit circle in the first quadrant, traced counterclockwise from (1,0) to (0,1). ∫c F*dr=

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A: Given I = ∫1-x2x3dx    ......... (1) Integration by parts ∫u(x).v(x)dx = u(x)∫v(x)dx…

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A: Our Aim is to define Fundamental Theorem of line integrals

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Q: Use the Fundamental Theorem of Line Integrals to calculate exactly. F-6 sin(ox +)+ sin(6x )j along…

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A: Given : I = ∫01∫sin-1(y)π21 + cos2(x) cos(x).dxdy To find : Value of given double integral Solution…

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A: To plot direction field we plot small lines with slope calculated form differential equation after…

Q: Use the Fundamental Theorem of Line Integrals to calculate 7. di exactly. F6 sin(6x + y)i + sin(6x +…

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Q: Set up an integral that represents the arc length of the function y = 4x4 + 5x from the point (0,0)…

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Q: Use a table of integrals to find the length of the curve y = x² from x = 0 to x = 2. %3D

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Q: Sketch the graph the integrands and use areas to evaluate the integrals. La |(1- l2) dx а. -1 3/2…

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Q: Evaluate the line integral $ x*dx + xydx where C is the triangle with vertices at (0, 0), (0, 6) and…

A: Given Line Integral is ∮x4dx+xydy , where C is a triangle with vertices at (0,0), (0,6) and (6,0)…

Q: express the length of the curve as an integral but do not evaluate it. r = sin3 θ, 0≤ θ ≤ 2π

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Q: Pls kindly help evaluating integrals by first differentiating Theorem Intergal(0,infinite)…

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A: Given integral is, .Integral is evaluated over the region E.

Q: Evaluate This Integral if curve C consists of curve C₁ which is a parabola y=x² from point (0,0) to…

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Q: a) by parametrizing C, b) by using the Fundamental Theorem of Line Integrals.

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Q: 4) Write the integral to calculate the outward flux through F = (-yx2, xy,-z) across the sphere with…

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Q: f(x)=sin(x)/x_between 0 and 1 using Trapezoidal

A: fx=sinxx Trapezoidal rule fx≈h2fa+2fa+h+fa+2h+---+fb a=0, h=0.05 and b=1

Q: image attached

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Q: 2. Estimate the integral using Simpson's approximation rule with n=4: sin t dt

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Q: use a double integral to find the area of the shaded region.

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Q: State the Fundamental Theorem for Line Integrals

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Q: Use double integral to find the average temperature of 1 (x, y) = tion of o ploto 0<rs4 and 0< y3 5…

A: Given,      T(x, y)=12-6x2-4y2,       0≤x≤4 and 0≤y≤5

Q: It is not possible of an integral of a function to be zero over a contour although the function is…

A: Yes it is possible,