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Q: If J_f{x)dx=10 andJ, f{x)dx= 3, then J, f(4 – x)dx=?

A: According to our guidelines we are supposed to do only one question. Kindly repost the other…

Q: Find r'(t).

A: We have to find r't: rt=4ti+t2tj+lnt2k We know that dxndx=nxn-1d lnxdx=1xd lnfxdx=1fxd fxdxdxdx=12x…

Q: 6 If x=25eco, y=4tan8. Evaluate dy where B= Lrad Ans/-0.2647

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Q: If x"y" = (x+y)* m, m+n d'y prove that = 0 .2 dx?

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Q: e the triple integral: (x+y+z)dydxdz 6 24 18 12

A: Topic :- application of integration

Q: SI. 1dV, where B = {(x,Y, z): 1 < x² + y² + z² < 4, y 2 0}.

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Q: Q.1B) If w = f(u,v) where u = tan"12 &v=In(x² + y²), the show that: dw Х- +- дх дw dw <-2- ду ду

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Hawis Find d Vand V2if vI+2V2=31-k and 3V-V2 si+j+k

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Q: dy Use separation of variables to find the general solution to dr + 4xy? = 0. %3D

A: We have to sine given differential equation using seperation of variables

Q: ; Use Gausss D.T. to evalu arte where F=4 xi -zy'i+zk auds is the sarfece bounding the regioh…

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Q: Fain the par hicul ar foluhion 4 DE . 9xy dy ; uh en x= 2,y=1 4xy° dy = 2y (1+ y?) dx ; when x- 2…

A: In this question we will use basic of calculus i.e contact of solution of differential equation. We…

Q: zl*dz, where C is x(t) t2, y(t) , t:2 1 Evaluate /=

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: D = {(x, y) E R² :0<x <∞, 0 < y<∞} olmak üzere, [ rye--v°dA D.

A: A multivariable function f(x,y) is a rule that is used to associate a number or quantity with a…

Q: C is given by x = t', y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + xdy + y dz) 33/20

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Q: - If y = e3x and y = e-3x , prove that: - %3D d²y 9y = 0 dx2

A: Given: y=e3x⇒dydx=ddxe3x⇒dydx=3e3xNow,d2ydx2=ddxdydx       =ddx3e3x       =3ddxe3x       =33e3x…

Q: For x,y E [0,1], prove that xy(1-x-y)≤1/27

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Q: C is given by x = t°, y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + x dy + y dz)

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Q: dy let y = xtan z then is da elect

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Q: Obtain ∫C  ez / (z - πi) dz with C defined as z(t) = 4eit and 0 ≤ t ≤ 2π

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Q: dz where c is |z=1 z'e? Evaluate

A: ∮ f(z) dz = 0 when no any singularity lies within region of integration. But if any singularity lies…

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

A: Given problem:-

Q: 198). Let c be (,0) to(4r, 0,0) G=) ydx+ xdx t Xyz dz Is 6CX Y,Z) independent of C?

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Q: If f(z, y) = e" sin(4y) then: V f( – 1, 1) =

A: Given function is f(x, y) =e4xsin4y.  We have to find ∇f(1, -1 ). The vector differential operator ∇…

Q: Compute |// a² d.x dy dz, where E = {(x, y, 2) : x² + y? < 1,0 < z < 1}.

A:

Q: ∫C  ez / (z - πi) dz where C is defined as z(t) = 2eit and 0 ≤ t ≤ 2π

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Q: 10. What is 2ri 2 fo, h (z) dz?

A: curve C3 encloses points of singularity z=-2 and z=0 in clockwise and counterclockwise directions.…

Q: dy where C is defined by dx + x2 + y? Evaluate x2 + y? C T(t) =,0 <t< 2n

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Q: || (z, y) dy de = f(r,y) dx dy 0. Jo Jo O Tryc

A: Solution: The objective is to select the correct option

Q: d²y Given that x +y³ = 2, prove that dx2 4.

A: Given: x3+y3=2   As we know that; The Power rule: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2

Q: 2. у"dy 3D х (хау — уах)еу 3. ydx %3D х + Vу? — х?dy 2 (1n In v) d, - y (1ulny ulnr) di

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Q: If y= Vx (x-1), find dy (Use rules, not a XP de finition

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Q: Prove that c?p?-(jx² + jy²+jz³) is the invariant quantity equal to c?po?.

A: Consider the provided question,   Prove that c2ρ2-jx2+jy2+jz2 is the invariant quantity equal to…

Q: f[x'+zy2,y²2x2], then prove that [y?-zx] (a?-yz] dy [z-xy] du -o. If

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Q: dæ is equivalent to Using the substitution u = x + 1 Vx + 1 1 -du 1/2 du du -1/2 du - 1) /u2

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Q: Evaluate SSS 2e(a²+y²+z?)"² dV over B where B= {(x,y, z) : x² + y² + z² < 1}. Take n = 3.

A: • The given region B has spherical symmetry, so it will be easy to solve this volume integral in…

Q: Given Yy - y = – ỹ Yy - y + y. - ỹ and (y — У )? [(Yj – J,) + ỹ, – ỹ )]² 2. %3D

A: Given that

Q: dz where a inside r= C z-a 2ni

A: We have to find integration of given function Using Cauchy's Integral Formula.

Q: g(x) = Af(Bx), where: %3D A = %3D B =

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Q: I For flay 2) = Vxy?z +4x*y, xy,?>0, compute and

A: Both differentiation are solved.

Q: "ind where f(x, y, z) = e²´y and x = Vuv, y = ; %3D dv

A: To find the partial derivative using chain rule

Q: Find ∫C  ez / (z - πi) dz where C is defined as z(t) = 4eit and 0 ≤ t ≤ 2π.

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Q: BeR NOULLI 's EQUOTION (2yーX)d水+ラ×ydy:o ソ+PCx)yq(x) yh XrlwDepenとn 3 y= Depen Dest

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Q: Find f f'Lx) = ZR? +aX-S and %3D to FlO)=4.

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Q: if y' - y =2x Then, d'y -24y prove that dx (3y –1)

A: Given that: y3-y=2x

Q: f (г, у) — In(ax + by) a, b ER af Land 1 Find Ja 2. Find and a f -and 3. Find dxðy дуда

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Q: Q2: Given y = f (u) and u g(x), find dy/dx: y = 2u3, и %3D 8х — 1

A: Differentiate