The area of the surface obtained by rotating the curve y = 1

Q: If f(x, y) = y° cos(x) – x³ In(y), find the second partial derivative ду дх .A ² f ду дх 3x2 -2y…

A: Calculate partial derivatives

Q: Find the area between the curves y = 4 cos(6x),    y = 4 sin(12x),    x = 0,    x = π/12

A: Given,

Q: What value of b > -1 maximizes the integral function

A: Given,

Q: Find the area of the region between the curves y = sin(x), y = sin(2x), x = 0, and x = t/2. Area…

A: Given curve is : y=sinx   .......(1) y=sin2x   ......(2) To find the area of region between curve…

Q: 0. Inx dx -2

A:

Q: Find the requested partial derivative. dz 3 if z° = z+ xy - 1 and y = x+ y- 1 dy 3

A: We have to find partial derivative

Q: . Form the differential of the system of circles touching the y-axis at the origin.

A: The solution is given as

Q: Evaluate (2x-y)dx+(x+3y)dy along the path C: curve on y = 1-x² from (0,1) to (1,0).

A: Given the line integralI=∫C(2x−y)dx+(x+3y)dyCurve y=1−x2

Q: For z = arctan(x² + y²): Compute all first and second order partial derivatives. Find the…

A:

Q: Find the partial derivative. (2² + 4x – 4y)* z = dz

A:

Q: nich integral represents the length of the graph of y = In(1 – x²) over the interval [0, ]:

A: here option A is true because length is given by =1+(dydx)2dx so here…

Q: (a) Use the Midpoint Rule with n = 6 to approximate integral S³ dx 8 x-6 6 x+8

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: 1: A)find the length of the curve y=3(x)/2 – 1 from x=0 to x=1 ? B) Prove that: cosh (x + y) = coshx…

A: A) Length of the curve is y=3x32-1 B) Trigonometric function

Q: Queston} $²3 20c x²-4 Composite Trapezoidal rule with n=4 dx. 3.1.1. use the to approximate…

A:

Q: Evaluate the integrals using partial fraction 3y²-y+! S y³ - y² dy

A:

Q: Evaluate the integral. 1//3 3earctan(y) dy -V3 1 + y2

A:

Q: (1,2) (b) Set up a definite integral that is equal to the arc length of the portion of the circle…

A: Note:- As per your request i am solving here question no. 3 part B only.

Q: express the length of the curve as an integral but do not evaluate it. r = (2 − cos θ )−1, 0 ≤ θ ≤…

A: Definition used -                Length of the curve -            L=∫αβrθ2+r'(θ)2dθ

Q: Compute the partial derivative fxxyz for f(x, y, z) = cos(cos(x3 + z2 )) + x2 ln(y2 + z2 ).

A:

Q: If f(x, y) = y cos(x) – a° In(y), find the second partial derivative ду дх .A 3x2 = -2y sin(x) ду дх…

A: Option (a) is correct.

Q: integral of sqrt(9-x^2)(x)dx. limits are from 0 to 3

A:

Q: Let z = z(x, y) be a continuous function of x and y defined implicitly by In(3æ* + 4y* + zyz*) = =…

A:

Q: Find the indefinite integral using the Chain Rule/U-substitution. 6x dx x2+5 3. 4. S 7xv3x² + 8 dx

A:

Q: Find the partial derivative of f(x,y) with respect to y at the point (3,2) f(x,y) = ln(x^2y-xy^2)

A: A partial derivative of a function of several variables is its derivative with respect to one of…

Q: he integra = 3/2 is dz Z-2

A:

Q: Find the partial derivative. = (a² + 4x – 2y)° - dz II

A:

Q: Find the area under the curve y = sin √x /√x between x = π^2/4 and x = π^2

A: Given function

Q: 2 (F(x) + x³)dx = ? %3D -1

A: Given that the area under f(x) in [-1,2] is 10br2 So,

Q: Use the Midpoint Rule to approximate the integral 13 | (- 2x + 10æ²) dx with n=3.

A:

Q: Use the Midpoint Rule withn= 3 to approximate the integral %3D 13 (- 9z - 3a")daz 9x 3x) dx

A:

Q: 1. Find the area of the region bounded by the curves y=sin X16 , y = 0, and x = 6 obtained by…

A: topic - Area bounded by curves

Q: What is the result of the partial derivative 3(z² + y sin (z)) Select one: a. 2a + y * cos(x)

A:

Q: (5)Obtain the integral curve for x 2+y = x passing through the point

A:

Q: THE AREA BETWEEN THE CURVES 4 y = x²³² AND y ²³ = 4X IS REVOLED 2 ABOUT THE LINE X= -1. SOLVE FOR…

A:

Q: Consider the curve defined by the equation y = 5x + 1x. Set up an integral that represents the…

A:

Q: Find the are length of the curve y² = 3x between the from x=0 to x=9 ! Use integral approximation!…

A:

Q: Find the area under the loop of the curve y2=x4(x+4) using integration

A: An integration formula for calculating the area under the curve will be used. We will calculate the…

Q: 64 ans: su 3 6. Calculate the area between the Curve fcx) = x²³²_4 and the lines y=2x + 4 and y=0,…

A: area between curve

Q: 5. Find the area enclosed by the inner loop of the curve r = 1-3 sin 0

A: Area Between Functions With Integration: The interval of the inner loop of the given polar curve is…

Q: What can you conclude about a real function f(x,y) that has continuous partial derivatives at a…

A:

Q: Show that the differential form in the integral is exact. Th (1,2,3) | 2xy dx + (x² -z°) dy -6yz dz…

A:

Q: An area is bounded by the x^2+10y-1600 curve  and the -xaxis. Find the moment of inertia (in units4)…

A:

Q: 2x lerivatives from first principle, find the derivatives of y = 5 V3x-e2x-(xln x)(In(In x)) -2e2x)…

A: We have to find the derivative from the given function

Q: 2. Use the Midpoint Rule with n = 4 to estimate (x² + 1) dx %3D

A:

Q: FIND THE PARTIAL DERIVA TIVES OF z = x cos (y- x )

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: What is the I.F of (x^2y^3+2y)dx+(2x-2x^3y^2)dy=0?

A: Find the integrating factor

Q: Use the Midpoint Rule with n = 4 to approximate the integral. %3D 14 x2 dx

A: We have to solve the integration using mid point rule.

Q: 3. Estimate the value of the integral 1 dx (n = 4) using Trapezoidal rule. 1+ln x

A: The value of h in the trapezoidal rule is h = b-anh = 5-34h = 24h = 0.5 Form a table with the x…

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (4, -3)

A: To solve the given line integral.