Evaluate [R(5xy + z²)dV, where B = [-10, 10] × [0, 1] × [0, 10]

Q: Evaluate the integral fa* (2* – 11)"dz, dx, by making the appropriate substitution: u = 11). 24 dx =…

A: ∫x3x4-1124dxSubstitute u=x4-11du=4x3dxdu4=x3dx

Q: Evaluate the integral dx (3x + 15)²’ by making the appropriate substitution: u = dx + 15)?

A: To evaluate:∫dx3x+152

Q: -1-y 3) Evaluate the integral dxdzdy?

A:

Q: Evaluate the integral dx (5ӕ + 10)2 by making the appropriate substitution: u = dx (5x + 10)? II

A:

Q: Evaluate the integral fa*(2* – 2)" dz 15 by making the substitution u x4 – 2. -

A: Given : ∫x3(x4-2)15dx

Q: The evaluation of the Integral of S x² V1- x dx is 105 V (1 – x)³[15x² + 12x + 8] + C (ii) V(1 –…

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Let H(x) integral ,for -2 ≤ x ≤2.Find the value of s such that H(x)= sH(-x).

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Q: Evaluate the integral dx 2xx - 3x? A -In 4 V2x + V3 +C 1 V3+ 2x B In +C 2/3 V3-2 +C In 2/3 "/7x + /3…

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Q: Evaluate L 8y (x³ + 1)² 2y by reversing the order of integration. dady

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Q: In ABCD, H is the centroid. If HF=6 find BF. C E

A: It is known that the centroid of a triangle divides the median in 2:1 ratio. It is given that HF=6.…

Q: Evaluate the integral: Jxe dx хе -2x -xe -Xe 2x +C -Xe2x e -2х —хе +C 4 Xe 2: -2x хе -2x e +C -2x…

A:

Q: Evaluate the integral: tejat A. 2 1n(e2t-e-2t) +C B. 2 1n(e2t + e¬2t) +C e20-e-2t In(e2t-e-2t) +c -…

A: To evaluate the given integral.

Q: Evaluate the integral: r+∞ 1 dv v²+2v-3

A: We will find the integral.

Q: Evaluate the followingintegrals.∫(z+1)√(3z+2)dz

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Q: what is the integral of e^(-2a|t|) from -w to w?

A:

Q: Evaluate the integral *(* – 10)"dz 6 by making the substitution u = 1 z° – 10- +C

A: ∫un du = un+1n+1+C ; where 'C' is an integration constant.

Q: Find the total differential z = 2x3y − 8xy4

A:

Q: 9. Evaluate the integral // V2 + y² + z² – 3 dV where S lies between a² + y² +2² = 1 and a? + y² +…

A: Given integral, ∭sx2+y2+z2-3dV Where S lies between x2+y2+z2=1 and x2+y2+z2=9. The spherical…

Q: a+bx² dx V3ax+bx3

A:

Q: c) Evaluate | V In(z)dr by using integration by part.

A:

Q: Find the integral. |(2x3 - 3x2 + x – 1) dx A x² + B 6x2 - 6x + 1 + C (c) None of the above x2 - x +…

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Q: The integraing factor of (4xy+3y² – x)dx + x(x+2y)dy3D0 is (A x-2 B 2x-2 2x-1 D D x2

A: Since, the given differential equation is not exact . To make it exact we find integrating factor ,…

Q: Evaluate the integral.

A: Given integral: ∫121241-x2dx

Q: Find the antiderivative

A: Consider the given integral

Q: Evaluate the integral S dx 2x3 - 3xx 1 -In 2/2 "I/3x + /2 +C En(2 { x³ - 3x x)+c 1 V2 + V3x -In + C…

A: First we take common x3/4 then put√x=t  And using integration of 1/a2 - x2

Q: Prove that Jn (x) X good dx=1. n

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Q: Evaluate the improper intergal 1 dx using the residue (x² + 16)² theorem.

A: We need to evaluate integral.

Q: Evaluate the integral f 2x (x2 + 7)° dx using the substitution u = x2 + 7. 2.x (x² + 7)° dx +C

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Q: Evaluate the integral f 2x (x² + 3)° dx using the substitution u = x2 + 3.

A:

Q: Evaluate the integral (2a+4)(x² + 4x + 2)*dx 4 by making the substitution u = x+ 4x + 2. ,2

A: Let u=x2+4x+2, now differentiate it with respect to x. du = (2x+4)dx So,…

Q: Find the product of the integral 1- S x²cos(xy)dxdy

A: We have to change order of integration first.

Q: y = sech*x = In(_+ V1- x², sechx = In(- 1+ V1-x² Prove that .... ..

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Q: Evaluate the integral dx (7x + 6)2 by making the appropriate substitution: u = dx (7x + 6)

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Q: Use the substitution formula to evaluate the integral. Vx +1 dx B) 2/2 - 1 D) 3/2 - 3

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Q: Use the substitution formula to evaluate the integral. fin-√3/22 c2x dx 1 + e4x 28) 0

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Q: Show that 3x2 +6x +2 = 3 (x+1) - by completing the square. Hence, evaluate the 2 integral dx. V3x? +…

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Q: Find the derivVative of the function. 5. y= In 8v +5 dy dv %3D

A: The objective is to find the derivative of the function.

Q: Evaluate the integral. dx J2 (x² – 1)3/2 -Csc O

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Q: ar integral of the c 3 – 7D2 + 7D – 2

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Q: ydzdydx x²+ y² +z? 2.

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Q: 10. Using the substitution u 2x - 1, prove that %3D 3 8 dx J1 (2x-1) 25

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Q: In evaluating / x(4 – x)ŝdx , if we use the substitution that u = 4 – æ, then what will be the…

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Q: Evaluate the double integral. 8xy2 dA,    D is enclosed by x = 0 and x = (4-y^2)^1/2

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Q: E valvate cox³ (x²+3)dx 2.

A:

Q: Expand, that is, perform the indicated operations on the differential operator D. 1. xD(R+ x)

A: Given that         xD(D+x)  Here we have to expand this and perform the indicated operations on the…

Q: evaluate the Cauchy principal value of the given improper integral. roo 1 dx 6x + 25 | roo x2 dx (x2…

A: The Cauchy principal values of the given improper integrals areevaluated as shown below.

Q: Use the substitution formula to evaluate the integral. 2/5 dt v/252 -1 -2/5

A:

Q: (х3 + 2у — z + 3) dxdydz 0, 1 2

A:

Q: Q2: Evaluate the integral S Vx² – 2x + 1 · dx 3,

A: To Evaluate: