Evaluate the integral 35 dz 4 by making the substitution u = x* – 6. +C

Q: Evaluate the integral. 6. 9 In(y). dy Vy J4

A: Given,             ∫49lnyydy

Q: dz 2 t´ + Zz-3

A:

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

A: To evaluate:∫dx3x+152

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

A:

Q: Find the general integral and compute 3 diferent solutions for : xzx+(x+z)zy=y-x

A:

Q: 1 dɔ V9-x² 3

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Q: Evaluate the given integral with suitable substitution : 5z 10r (20 + 20) dr

A: Explanation of the solution is given below...

Q: Evaluate the iterated integrals: 4 2 S[x* +xy}dydx 0 1

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Q: Evaluate the integral by making the given substitution. sec(6z)tan(6æ)dr, u = 6z + C

A: According to question given :∫sec6xtan6x dx, u=6xWe have to evaluate the integral by making the…

Q: Evaluate the integral da 2+ et using the substitution u = 2+ eª. dx 2+ et +C | -

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: Evaluate the integral 24 11) dx, by making the appropriate substitution: u = Ja* (2* – 11)*“dz =

A: ∫ un du =un+1n+1+C

Q: Find the integral of r(t) = (3t2 + 4t, 2, e') from 0 to 1.

A: Consider the following vector: rt=3t2+4ti^+2j^+etk^ Integrate the above vector:…

Q: Evaluate the integral. (2 + 2y)? dy

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Q: Evaluate the integral 20 | by making the appropriate substitution: u = 5 – 2 (2³ – 2)® dx %3D -

A: Evaluate the integrals

Q: Evaluate the integral using the given substitution. 18(6x- 2)6 dx , u = 6x - 2 0.(6x - 2) +C O (6x -…

A: The given integral is ∫186x-2-6dx and  u=6x-2

Q: Find the product of the integral In(3) S Som) xy e*y* dxdy

A:

Q: Apply Green's Theoren to evaluate the integral. C6x+y) dx + (3xy"+4y) dy ter

A: Given integration is ∮c(6x+y3)dx+(3xy2+4y)dy C : Any simple curve in the plane for which Green's…

Q: Evaluate the integral (= - 11)" de, 26 by making the appropriate substitution: u = 26 |- NOTE: Your…

A: Proceed as shown below...

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

A:

Q: Use the substitution formula to evaluate the integral. T/16 (1 + etan 4x) sec 2 4x dx 4e

A: Given that ∫0π161+etan4x sec24x dx ...........................(i) Substitute u= 4x  dudx=4 ⇒dx=du4…

Q: Evaluate the integral fe (2x+4) (x² + 4x + 2) dx n- by making the substitution u = x²+ 4x +2.

A: In the question we have to find the integral of the given function.

Q: Evaluate the integral x3 dx 2+100 S x3 dx +100 (Use C as the arbitrary constant.)

A: Given,

Q: (d) Prove that 1-cos 2x dx is divergent. Hint: Split the expression inside the integral into two…

A: Integral is converges or divergence

Q: evaluate the integral.

A:

Q: Solve the double integral J, J, (1+ xy)² dydx In n(금) O 2ln(5) – In(3) O In(3) – 4ln(5)

A:

Q: Evaluate the improper iterated integral. • 1/x9 y dy dx Jo

A: In this question we have to evaluate the integral.

Q: Estimate the errors in the approximations for T10 and M10 of the integral from 1 to 2 of e1/x dx,…

A:

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

A: I have use the substitution

Q: Evaluate the integral [x²y³² (x²y + xy² + y²²)dxdy dz 001

A: The given triple integral is ∫01∫02∫13x2y3x2y +xyz+yz2 dx dy dz. First integrate with respect to x…

Q: +00 dx Evaluate the improper integral x(In x)²

A:

Q: Evaluate the integral dx (4x + 14) by making the appropriate substitution: u = dæ (4x + 14)* Submit…

A:

Q: Evaluate the integral. 2 - 121 y - 121 2 -dy, y> 11 dy=

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

A: To evaluate the given integral.

Q: Evaluate the integral 1 2-x xy dy dx 0 x2

A: Here we have to evaluate the given integral

Q: Suppose we perform the substitution u=1+Vx in the integral dx . (1+Vx)5 What is the resulting…

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Q: 1 dz c+x2 c)

A:

Q: Evaluate the integral dx (2x + 4)* by making the appropriate substitution: u = dx (2x + 4)°

A:

Q: Evaluate the integral. Clearly indicate u-substitution steps if required. 19 J2+ 5y

A: Given integral is ∫195+2ydy evaluating the integral with u substitution

Q: Evaluate the integral (x – 1)ez xp- x² – 2x + 2

A: The objective is to find ∫-∞∞(x-1)eix(x2-2x+2)dx It is known that, eix is an increasing function.…

Q: Evaluate the integral from 0 to 1. 3/(1+t2)j + 5t4/(1+t5)k

A: We first separate the integrals. ∫3(1+t2)j+5t4(1+t5)kdt=3∫11+t2dtj+∫5t4dt(1+t5)k=3arctan(t) j +…

Q: Evaluate the Cauchy principal value of the given improper integral. 1 [ (x² + 4)² dx

A:

Q: Evaluate the integral. 7 - x2 | x5y dy

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Q: Evaluate the integral of ((x dx)/(x + 1)8) from o to 1.

A:

Q: Evaluate the improper integral dz, if it exist (x² + 49)2

A: Here we have to evaluate the given improper integral.

Q: Evaluate the integral. X √ ² ₁x + (x + 16y) dy

A:

Q: Evaluate the integral. 10 r FIL √16 22 1 (x² + y²) 1/2 dy dx dz =

A: To evaluate the integral ∫04∫-44∫-16-x216-x21(x2+y2)12dydxdz

Q: Evaluate the integral.

A: Evaluate the integral.              ∫04-x2x2ydy

Q: Evaluate the integral of ax^2 e^bx dx assume a and b are constants.

A: Please see the explanation below