Evaluate the following integral in cylindrical coordinates. 5 342/29-x² -x2 -y dy dx dz 5 3/2 /2 9-x² e -x2 -y dy dx dz = (Simplify your answer. Type an exact answer, using x as needed.)

Q: Q5: A) Evaluate the following integral : S(z? – z-2)² + 4 dz B) Find the slope of the line tangent…

A: To evaluate the integral, the function z2-z-22+4 has to be first simplified. Now, z-2 can be…

Q: For long cirular cfinder of Re two halves maintained at temprature U1 and Vi respectively, Show that…

A:

Q: 1 Use the Trapezium Rule, with seven ordinates, to evaluate In(sin.r+3)dxcorrect to four decimal…

A:

Q: y = In x3 sinx 2 Cx² + 4

A: The function is given by y = lnx3sinxx2+4 To evaluate: The expression of dydx.

Q: 2. Use cylindrical coordinates to evaluate √√9-x² 9-x²-y² [dz x² dz dy dx. √9-x2 0

A:

Q: solve part (d) Consider the ellipse +5 = 1. (a) Show that the circumference of the ellipse is given…

A: Suppose u=gx and g' be a continuous function on a,b and also f is  continuous over range of the…

Q: iven: v(t)=t"-2t in m Iscc where os ts find the displacement of this objcct

A: Find the particle's displacement by integrating velocity function:

Q: Find S y? sin y dy

A: Given,            ∫y2sinydy

Q: TT x sin y dydx 0.

A: Given: ∫01∫0πxsinydydx Evaluate the integral. ∫01∫0πxsinydydx=∫01xdx-cosy0π=∫01x2dx=2∫01xdx

Q: Solue D.E dy + (y cotx Sina) de = o

A: Solving

Q: d) y = sin*(x'/3) + arctan(r?)

A:

Q: H.W: Solve B.C Ans. سے لے 2 dx² y = X dx X² ylı)=1 = y(2)=2 Use h=0₁/ y (1.5) = 1.481159 + Sin(Lnx)…

A:

Q: Determine the moments of inertia of the shaded area about the x- and y-axes. 1 0 Answers: -x

A:

Q: 9. For each n E IN, let Xn be the set of polynomials of degree equal to n, and let Pn = U_0 Xk. True…

A:

Q: 2. Find (in terms of t): x = 2 + 3 sin t y = -1+4 cos t

A: Given data is : x=2+3 sinty=-1+4 cost To find the value of d2ydx2

Q: Iidydx.

A:

Q: Rewrite the equation with the variables separated. dy + Vỹ = e# /G dx dy (e – 1) dx dy (e + 1) dx dy…

A: Rewriting the equation with the variables separated.

Q: the non homogemesus. equation Salve メ++5 2x +24+7 ot x

A:

Q: Q.IH s= 1-csct , find value of ds 1+csct dt

A: Given, s=1-csct1+csct Quotient rule of differentiation states that ddxfg=f'g-g'fg2

Q: Suppose the velocity of a particle is given by v(t) = (sin(4t), 3 cos(t), 4t³). Find the…

A: Suppose the velocity of a particle is given by v(t) = (sin(4t), 3 cos(t), 4t³). Find the…

Q: Find the Laplacian of cylindrical coordinate p?cose.

A: Given form is in cylindrical coordinates.

Q: 1 dx = arcsec(x – 3) + c - (х — 3) Vx? — 6х + 8 6x + 8 -

A: