(Compute Sc (-3y+ony Sin(3))dxt (5x²-(ye)du Where C is a Simple Clased cUne in the plane oriented counter Clockwise, that encloses a region of area 8.

Q: Evaluate the integral (2æ + 6)(x² + 6x + 9)*dx by making the substitution u = x? + 6x + 9. + C

A:

Q: 4. Integrate: 5dx dx a) f b) [ c) f- 1 dx; d) x' V16-x? 1+ cosx cos x

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

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

A:

Q: 2 cos Ø sinotos"0 csc0 Reuorite the expresson as a single triganometrie function whose anqument is…

A: Given: The expression 2cosϕsinϕ+cos2ϕcscϕ, To simplify: The given expression in term of one…

Q: Evaluate the impropec integral oc sho that it diverges, dx

A:

Q: Compute the Jacobian for the substitutions x = p sin cos 0, y = p sin Ø sin 0, z = p cos 0.

A: Step 1: Step 2: Step 3: Step 4:

Q: Q2. If f(x, y) = xy² + y²cosy + xsiny then a) y² - siny c) 2y + cosy a²f is дудх b) y² + cosy d) 2y…

A:

Q: Given z=4x² + y2 -2 and C: x=cos t, y= sin t for [0,2] a) Find z'(t) using chain rule (not…

A: ### Part (a): Finding  z'(t)  using the chain ruleGiven the function  z=4x2+y2−2  and the curve  C…

Q: 4.) evalnate the integral dx aresinx a. WI-Y b) S x arctanx dx

A: We have to solve

Q: dx + AIX y = cos x, y(n) = 0

A:

Q: Let fx,y) = xcos(xy)+ y'. Which of the following is true?

A: Given function - f(x,y) = xcosxy3+y7Differentiating with respect to x - fx=ddxxcosxy3 + ddxy7fx =…

Q: Compute where Cis the counter clockwise oriented boundary of upper-half unit disc D. 0.66666666667…

A: We need to find ,  ∮ y2dx + 3xydy , over  C ,  where C is the counter clockwise oriented boundary of…

Q: Show that (6.g) = (0,0) is unijomy continuous or not.

A: Uniform continuity

Q: 4. Evaluate the iterated integral T, cos(³) dydx. a. (cos 1- 1) b. 1 e. (sin 1- 1) f. 1 (1- cos 1)…

A:

Q: What is the domain of r(s) = e*i+ sj+cos sk?

A: Given: rs=esi+sj+cossk We know that for given expression domain will be domain of s and for square…

Q: . If U = z sin y/x where x= 3r2 + 2s, y= 4r – 2s², z = 2r? – 3s², find a) Or b)

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Q: Integrate by parts [2x(x-3)* dx Formula: Sudv=uv-fvdu,

A:

Q: Use Green's Theorem to evaluate(¹-28) O-96 O-75 O 105 -2y) de- (62-4ry") dy where C' is shown below

A: We want to calculate the integral ∫Cy4-2ydx-6x-4xy3dy

Q: 2. Rewrite the iterated integral f(a, y, 2)dz dy dz in the order of -√1-z Jo (a) dz dy dr; (b) dr dz…

A: The given integral is, ∫01∫-1-x0∫0y2f(x,y,z)dzdydx. we have to write the iterated integral in the…

Q: 1. Evaluate the integral [dx A S dx Ady + 3dx ^ dz of the 2-form w=dx^dy+3dx^dz over the oriented…

A: We have to find the value of integral.

Q: 4.) Evaleuate the integrali Jóxarcsin(5a)dx

A: ∫fg'=fg-∫f'gAnd ∫sinnxdx=n-1n∫sinn-2xdx-cosxsinn-1xnsee below the answer and calculation

Q: Show that cos λx 2² +1 -dλ TU že 2 x ≥ 0.

A: Given: x≥0 To show:∫0∞cosxλλ2+1dλ=π2e-x.

Q: Compute the dz in the function z = ety sin (xy) A. dz = ze"(cos (zy) + sin (ry) dz+ ye"lcos (ry) +…

A:

Q: find the LCfor f) and UCPr F) 1D FCX)= Eo) or [o1J

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

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.