Use the Fundamental Theorem of Line Integrals to evaluate F. dR where x 1 (−2x + 1)²³ y +1 and C is the portion of the parabola y = −x² + 1 from (1,0) to (0, 1). F(x, y) = ( ln(y + 1) - 1 + y² + 1) +1

Q: Evaluate the line integral f3y² dx + z² dy + (16 - x²) dz over the quarter of the circle of radius 4…

A: Kindly refer to Step 2 for the solution.

Q: S²10 f(x) dx = -10, Use these values to evaluate the given definite integrals. 2 1) ²³ (f(x) + g(x))…

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Q: Evaluate the integral х3 dx x2 +49 х3 dх x2 +49 (Use C as the arbitrary constant.)

A: We substitute x^2+49=t, then the given integral become

Q: ntegral. 1 3t(2 – t)²dt -1

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Q: 1. Let f: R² → R2 be the function defined by f(x, y) = (x + 2xy, y² — x² − y). (a) Show that the…

A: If z=x+iy then equivalently we can write z=(x,y) if f(z) is a complex valued function &…

Q: For each of following equations find the general integral and compute three different solutions.…

A: We’ll answer the first question since the exact one wasn’tspecified. Please submit a new question…

Q: Consider the function f(x) = x(x² + 3)". (a) Use the Fundamental Theorem of Calculus to evaluate |…

A: (a) Consider the given function as fx=xx2+37

Q: anction of z = x + iy

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Q: Let (z-a)" dz where a € C and the parameterization of the curve is a = {|z| = r}. Apply the…

A: Hint: The statement of fundamental theorem  of complex analysis is: If a continuous function f has…

Q: 3 : F = 2yi + 3xj, 6 = ³x³ + 2xy, and h = y — 4x². Let (a) Find each of the following: F-V6 = Vh=…

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Q: Calculate the line integral f(3xy³ − 4x + 4y + 8) dx + (−3xy+5) dy, where C' is the rectangle with…

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Q: ● Q1/ Determine the integral of the vector function -2π [sin² (t) cos(t) i + sin(t)(cos² (t) j + 2k]…

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Q: The function f(x) = |ax - b| + c|x| : x in (-∞, ol where Find the

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Q: a) Let f(x) = 3x² + 2x – 3x-1 +72". Compute the integral of f. = x-1 and let h(x) = x² + 2x. Compute…

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Q: Find the derivative of the dot product (u(t) • v(t)) if u(t) and v(t) equal the following (see image…

A: Given vectors are we are to find the derivative of u(t).v(t)

Q: Let ƒ(z) = f(x + y) = (x² - y² − 2x) +i (2y - 2xy) be a complex function. Where is the function…

A: According to the question,

Q: Evaluate the line integral (5x + 8y)dx + (3x – 5y)dy along the - curve C : x = 10 cos t, y = 20 sin…

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Q: Find the complete integral of (p2 + q2)y = qz.

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Q: Prove f(x,y)=ln(x2+y2)1÷2  by laplace equation

A: Given: The function, fx,y=lnx2+y2 and the Laplace equation, ∂2f∂x2+∂2f∂y2=0.

Q: sin 3x (x² +16)² dx

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Q: kx _f(x) = ek

A: The Fourier integral of a function f(x) is defined as:F(ω)=∫−∞∞f(x)e−iωxdxTo find the Fourier…

Q: Ex.2. Prove that the complete integral of the equation (xp + yq - 2)² = 1 +p² +q² is (ax + by + cz)…

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