integral that line x = 0

Q: owing integral equal?

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Q: f sec¹ x dx

A: Integrate the integral sec7x .

Q: integral i

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Q: 75. F(x) : (t + 2) dt

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Q: What is the Fundamental Theorem of line integrals?

A: Our Aim is to define Fundamental Theorem of line integrals

Q: Find the most general antiderivative. show all work Integral (secx/secx-cosx) dx

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Q: Use Green's Theorem to evaluate the line integral

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Q: x = X, +(-

A: let the initial velocity be v0 , and the initial distance be x0 .and in time t , the new velocity…

Q: What change of variables is suggested by an integral containing Vx? + 36?

A: For, an integral containing  x2+36 we can change variable by substituting, x=6tanθ, As it will get…

Q: . Find the area of region between two functions fix)=sinx, g(x)-cos2x,-끌sxs을 %3D

A: The area between two curves A=∫abf(x)-gxdx sinx=cos2xsinx=1-2sin2x2sin2x+sinx-1=0sinx=-1±1+84=-1,…

Q: Find F (x). sin(x) F(x) = Jo 3VE dt F "(x) = %3D

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Q: The equation of line normal to f(x) = (x +4)^(1/2) at Q (0,3) is

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Q: Write down an integral expressing the length of the curve y = cos x, 2 2

A: Apply the below formula: L=∫ab1+dydx2dx

Q: sec² 0 de. 1- tan 0 Evaluate the improper integral:

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Q: 9. f(x³ - 4x)dx -3 (x²-1) dx 10. ₂

A: We have to find the integral

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

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Q: Use substitution to find the indefinite integral x +2x dx x4 + 4x² = 3 x+2x dx%3D x + 4x² - 3

A: We have to solve

Q: Explain how the Fundamental Theorem of Line Integrals and Green's Theorem are both similar to the…

A: Statement of fundamental theorem of calculus:

Q: Use substitution to find the indefinite integral. 2. zy5z 5z²-8 dz 2. - 8 dz =|

A: The given integral is: I=∫z5z2-8 dz

Q: Evaluate the line integral F.dr

A: In this question, we find the line integral for given vector function and parametric path.

Q: equation of line normal to f(x) = (x +4)1/2 at Q (0,3) is?

A: Given, f(x)=(x+4)12 To find: Equation of line normal to f(x) at Q(0,3)

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: Use substitution to find the indefinite integral. 2 | 5z² – 3 dz -3 dz =

A: Given: I=∫z5z2-3dz   ...1   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: Compare and contrast the Fundamental Theorem of Calculus and the Fundamental Theorem of Line…

A: compare and contrast the fundamental theorem of calculus and the fundamental theorem of line…

Q: Find the gradient of the function: y = (5x ln (x)/ 6) + x/3 at the point with x-coordinate 1. Give…

A: We can solve this problem as follows:

Q: Show that the function x² – y² 2ху f(x,y) = { x² + y² if (x,y)# 0 if (x,y) = 0 is continuous at…

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Q: stlon 5 Use differential to approximate the change in the value of f(x)= ° as e goes from 2 to %3D…

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Q: 1 dz z dx 1 dz z dx2 1 dz •Ex 7x Ix =| z dx3 Exe

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Q: dx 1 Vx + x3

A: Answer

Q: dz Use implicit differentiation to find 3x2 1+2y 33y+z x+2yz 323y 1+2y %3D 1+2y

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Q: Set up an integral that represents the length of the curve. X = Vу - 9у, 1 s y <4

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Q: Evaluate the indefinite integral dx: %3D

A: topic - indefinite integral

Q: derivative of y with respect to x. y= In (6 In x) dy dx %3D

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Q: find the derivative y= the integral from 0 to the square root of x 5tcos(t^4) dt show all work

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Q: TRUE OR FALSE? The given line integral is independant of path.

A: The given line integral is ∫C2xz3+6ydx+6x-2yzdy+3x2z2-y2dz Compare the above line integral with…

Q: Evaluate the folowing indefinite integral. 1 dx 5 2x dx = 2x = xp (Use C as the arbitrary constant.)

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Q: Find the differential of f(x, y) = 3+y² at the point (2, 3). df: ((3x^2)dx+(2y)dy)/(2sqrt(x^3+y^2))…

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Q: ċ alculate Flux of F= through from 13,0). to.lQ,3)]. ariented live segment upward. 10,3) 13:0)

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Q: if Zcand Zp is complementary function Particular integral for the equation f(x X F(x,y) respectively…

A: This is Partial differential equation.

Q: The thickness of the shell is a = 0.5 centimeter. Use differentials to approximate the volume of the…

A: Given:        a=0.5 cm       r=100cm     Volume of shell V=43πr3     differentiating on both sides…

Q: Find the area of the segment cut off from the curve y = sinx, 0≤x≤nt by the line y = 1/√2. HT 1/2 y…

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Q: Inx F (x) = So It dt %3D

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Q: Find the sign of the line integral.

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Q: Consider the curve defined by the equation y = 3x + 4x. Set up an integral that represents the…

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Q: Find area of circle whose eq is (x-3)^2 - (y-3)^2=4 using integration

A: Note: The correct equation of circle will be x-32+y-32=4.  The radius of the circle is 2 and center…

Q: Use fundamental theorem of calculus .4 –dx x In x 2,

A: Follow the steps.

Q: dy by implicit differentiation of 2r2 3y2 = 4?

A: