Express f, 4xyz dV , where E = [0,1] × [0,2] × [0,3] by using different orders of integration. Hence find the value of the integral , 4xyz dV.

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Q: | Va3+1 dx dy 0,

A: ∫01∫y1x3+1dxdy=∫01∫0x2x3+1dydx=∫01x3+1x2-0dx=∫01x2x3+1dx

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Q: 7. Change the order of integrations to find iterated integral (dydx. 2

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Q: x e* dx (1+х)2

A: Explanation of the answer is as follows

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A: The answer is given as follows:

Q: Use the appropriate technique of integration to compute the following antiderivatives.

A: Solution

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Q: 1) Express , 4xyz dV , where E = [0,1] x [0,2] x [0,3] by using different orders of integration.…

A: In the given question we have to find the integration ∫∫∫E4xyzdVwhere E=[0,1]×[0,2]×[0,3]  is the…

Q: 1) Express , 4xyz dV , where E = [0,1] x [0,2] x [0,3] by using different orders of integration.…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 19z3e? dz

A: Explanation of the answer is as follows

Q: Evaluate the integral. (Use C for the constant of integration.) In(Vx) dx

A: ∫lnxdx=∫lnx12dx=12∫lnxdxLet u=ln(x)du=1xdxdv=dxv=∫dxv=x

Q: 1) Express , 4xyz dV , where E = [0,1] × [0,2] × [0,3] by using different orders of integration.…

A: Integration.

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Q: Find the integrals using integration by parts. b. [ Vx In /xdx

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A: ∫01∫x1x2y7+1dydx⇒∫0=x1=x∫x=y1=yx2y7+1dydx The reversed order of the integration is…

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Q: 3x2 + 4x + 10 8. *) (2x – 1)(x² + 4)

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Q: Identify u and dv for finding the integral using integration by parts. Do not integrate. In(5x) dx u…

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Q: Evaluate the integral. (Use C for the constant of integration.) 7 In(x) dx XV 5 + (In(x))²

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Q: Evaluate the iterated integral by choosing the order of integration. '5 xe* + 4y dy dx Ji

A: To evaluate the integral by changing the order of integration: ∫01∫15xex+4ydydx

Q: 1) Express , 4xyz dV , where E = [0,1] × [0,2] x [0,3] by using different orders of integration.…

A: See the attachment

Q: Reverse the order of integration and then evaluate the integral. 1 dy dx 3-yA. O In 17 - 1 4 O In 17…

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Q: Evaluate the integral using tabular integration by parts. 1 | 7 x° V2 x+1 dx (2x + 1) (35x – 15x? +…

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.