3x -dx x4 + 1 Evaluate the indefinite integral. + C

Q: Show that if x, y are rational numbers, then x + y and xy are rational numbers.

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Q: 5z dv, where E is bounded by the cylinder y2 + z2 = 9 and the planes x = 0, y = 3x, and z = 0 in the…

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Q: 2x2 dv, where T is the solid tetrahedron with verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0,…

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Q: +*- 2x+ 2y = ? d²y +x2 dx2 dx3 %3D

A: In the question it is asked to solve the differential equation shown below.

Q: SSS (x+ yz?) dx dy dz v. 06x< !, 0£ys2

A: Given that ∫∫v∫x+yz2dxdydz, where v:0≤x≤1, 0≤y≤2, -1≤z≤3 Here, we will evaluate the given integral

Q: Integral of 2xln(1+x)

A: We will solve the integral.

Q: Evaluate the Integral 2. S V5 + 12x – 9x²dx - ANSWER: 2. (3x-2)v5+12x-9x²+9Sin¬13*- 2]+C (3х-2)

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Q: x3 dx ] x4 – 4x² + 13

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Q: 3. Evaluate 5 sin rdr

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Q: I = c2π sin² 0 0 5 + 3 cos 0 dᎾ .

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Q: dx (4x²+1)* 2.

A: The given integral is:  ∫84x^2+1dx Consider, x=12tanθ On differentiating both sides. dx=12sec2θ dθ…

Q: Thanks but I am not understanding the integral. Could you please write it out. I am not…

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Q: The distribution of actual weights of wedges of cheddar cheese produced at a dairy is normal with a…

A: Solution: Let X be the actual weight of wedges of cheddar cheese produced at dairy is normal with…

Q: 5. Assume that an ant moves on a plane continuously; that is, its coordinates x(t) and y(t) are…

A: (a) equation of unit circle can be written as - at (0.7,0.1) at (-2,3) we see the change in sign…

Q: Assume that f : R → R is such that |f(x) – f(y)| 0 one has that f(r) – r f(0) + (1 – A)r (b)…

A: Explanation Given - assume that f:ℝ→ℝ such that f(x)-f(y)≤λx-y for all x, y ∈ℝ and some λ∈(0, 1) To…

Q: Integral of | 4sinxcos cos |dx 1. J sin 9x cos4x dx J cos 2x cos (-x)dx 2. 3.

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Q: 2x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the plane x = 2. %3D

A: The given integral is ∭E2xdV. The region E is bounded by the paraboloid x=2y2+2z2 and the plane x=2.…

Q: Jrsin( x)cos(x)dx

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Q: 3xy dV, where E is bounded by the parabolic cylinders y = x² and x = y and the planes z = 0 and z =…

A: It is given that, y=x2 and x=y2 and the planes z=0 and z=7x+y. Define the region E as follows.…

Q: (x - y) dv, where E is enclosed by the surfaces z = x² - 1, z = 1 - x², y = 0, and y = 4

A: Consider the given function fx,y,z=x-y.  The region E is enclosed by the surfaces…