[x xf (x²) dx Which integral is equivalent to the one shown: Oa) f f(u) du √uf (u) O b) S 2 O c) [ f(u) d 2 Od) √ √uf(u) du du du

Q: [2². X V2+xd.c

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Q: vinarixinvaxana Pic г.) 4. Find Brune fronor. [

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Q: Given f(x, y) = x³y + 7xy². Compute: 8²f 8x² 8²f by²

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Q: Evaluate each of the following Indefinite and Definite Integrals: a) ₁12x³-9x² + +2 dx

A: The given integral,a) We have to calculate the integral value.Note:Since you have asked multiple…

Q: By using trigonometric substitution, evaluate the following integral IVF x √²+6x+10 dz

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Q: y = √2+7tanz

A: y=2+7tan⁡x

Q: Evaluate the integral S√x Inx dx 3 2 4 -x² Inx+ x² + C 03x³nx-x²+c 4 2 -x² Inx+ 2 C 15 3 2 4 °²x²nx…

A: We have to solve above integral

Q: L? + y) da + (x + y?) dy ; C: AB, A = [1,3] → B = [3, 0] C: AB , A = [1, 3] → B = [3,0]

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Q: Exatuate the integral QUS √3x xام واح

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Q: 4. Explain how the following formula d (u₁-u₂-..- U₂) ² dx enable us to differentiate any…

A: The given formula is:ddxu1-u2-...-un=du1dx-du2dx-...-dundx. To Do:We have to explain how this…

Q: Prove that: f(æ) J. F(2) + f(a + b – x) b - a 2

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Q: d²y Given that x3 + y³ = 2, prove that 4х %3D dx2 y5

A: Given problem:-

Q: √2-y² X √x² + y² dx dy

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Q: x¹ + x² + 1 I(x² + 1)² -dx.

A: The given integral is: ∫x4+x2+1xx2+12dx Evaluate the given integral.

Q: e2" – e5r dr dx b)] Jx (1 + x) + e3r

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Q: Given that D/d = √f + p/f – p, express p in terms of f, d and D

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Q: integral: 24x² √64 – x² dx

A: ∫ 24x264-x2dx

Q: 4 xdx J(x+1)(х +4) 2

A: Here we have to apply integration by partial fraction method. We have the formula,…

Q: Evaluate the Cauchy principal value of 2x² - 1 fo dx. x4 + 5x² + 4

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Q: Exatuate the integral pvz O√3 √4-X² √EX 9 (√x ² + y² dy dx

A: Evaluation of double integral by conversion to polar coordinates.

Q: dx Find ; a2+x2 Find S x² + Vx – 2 dx Find Sx²e=* dx Find ſ e5x+2 dx

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Q: Evaluate the integral 9x² √x² + y² dzdy dx

A: Given problem:-

Q: dy : Find if dx 3.x 2) x - y 4+ y x +y 4) xy² x - y

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Q: ry? Find I.A. -dA, R= [0, 4] × [ – 1, 1] г? + 1

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Q: Iff, g e R(x) on [a, b), prove that f? dx + g? dx 2 2 Ifg | dx.

A: Given that, f, g∈Rx on [a, b]We need to prove that∫abf2dx+∫abg2dx≥2∫ab|fg|dx

Q: 4x³ – 3x dx 2x2 + 5 x4 –

A: