EX, chang to polar and evaluate I= f dy hpxpx

Q: ye(2y*) dy

A: Given the integral I=∫ye2y2dy     ....(1)

Q: z = tan¯1(4 – j7)

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Q: to polar coordinates r²+ y² dxdy turns into integral. when converting the integral.

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Q: Sinlxy). lnx dx 19141 to be investipa te the uniform Convergence of ne parametric intepral)

A: Given integral is, ∫01sinxylnxxdx Since, the given integral is improper integral so applying the…

Q: y = ay +b cos(wt) Scale and non-dimensionalize: C1 C2 Pick c1, c2 + change variable

A: We have to define this partial derivative in terms of x and t

Q: Consider the parametric equations x= 0 + 2 sine and y 1+ 6 cose. Which of the following represents…

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Q: 4–x2 Sở SY dy dx using polar Evaluate 2x-x2 Coordinates.

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Q: 45. The rectangular equation x² + y² - 2x=0 written in polar form is r = 2 cos.

A: The rectangular equation is x2+y2-2x=0

Q: Given the polar function r = {a(1-e^2)} / {1+ecos(theta)} find an expression for dy/dx, simplified…

A: Given that r=a1−e21+ecosθ To find an expression for dy/dx.

Q: 4. Convert to rectangular coordinates and sketch the curve x = 4 sec 0 y = 3 tan 0

A: Here we convert parametric equation in rectangular equation. And then we draw the graph.

Q: dy IN QUESTIONS 1-13, FIND dx' 8. y = tan8x

A: The solution is given below.

Q: Change into polar co-ordinates S Va²-x2 Lzdydx, and evaluate.

A: From the given integral: I=∫-aa∫-a2-x2a2-x2dydx The limit of integral, clearly shows that y varies…

Q: The student should answer the question below: Evaluate the given function using polar coordinates…

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Q: Evaluate ¹ (x²+x²2²)dzdx by using polar coordinates.

A: We have to evaluate the given integral using the polar coordinates. First we have to identify the…

Q: Consider the parametric equations x =t - sint and y = 1- cost. Which of the following dy ?…

A: If the parametric equations are  given byx=t-sin t  and  y=1-cos tThen to find the value of dydx.

Q: polarform - What is the average of (2 L2) and (24358)?

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Q: Classify the ODE’s according to their linearity. Write the name of the equation and find their…

A: Given: eycosx-xydx+eysin x-x22dy=0

Q: Eliminate the parameter for the given parametric equations to write an equation in the form of y=…

A: Given x=ln t and y=et

Q: Clasify elliptic, hyperbola forms. the following equation into and parabola Sin 2x Uxx + Sin Sin 2x…

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Q: п 4. Find the slope of the tangent line to the polar curve r = 1 – sin40 at 0 = 4 : a. 3 b. 4 c. 2…

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Q: to polar coordinates + y² dxdy J turns into integral. when converting the integral.

A: I have done solution in detail...go through the solution

Q: Given the polar function r = f(theta) = 4sin(2*theta) Find the average rate of change of "f" between…

A: Step 1: Step 2: Step 3: Step 4:

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: