parametrically

Q: Find the area of the segment cut off from the curve y = sin x, 0 ≤ x ≤ ¹ by the line y = 1/√2. 3r 4…

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Q: line with a constant acceleration of -8 ms 2. A De in the direction that the particle is initially…

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Q: Express the length of the curve as an integral but do not evaluate it. r = sin θ cos θ, 0 ≤ θ ≤ π

A: We have givem expression r=sinθcosθ, 0≤θ≤π We have to set up the integral for calculate the length…

Q: Explain whether integration by parts may or may not be used to evaluate the integral fx cosx'dx. If…

A: Indefinite Integration

Q: 2. Find the coordinate of the points on the cardioid r=1- cose at which there is a horizontal…

A: We are given the polar curve: r = 1- cosθ use formula:         x=r cosθy=r sinθ then,  dxdθ=-sinθ+2…

Q: Sketch the recion enclosed by the given curves. Decide whether to integrate with respect to rwr.Daw…

A: Draw all the regions first then decide which region satisfy all the curves

Q: rea under the curve y = 2x – x² from x = 1 to x = 2 with n = 4 %3D tonglon

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Q: 5. Find the area and centroidal distances of the curve that lies between he equations y%3D4-x^2 and…

A: The region bounded by curves y=4-x2andy=x+2 To find the area and centroidal distances.

Q: z² +1 dz 2²(z – 1) K

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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: A stone, projected vertically upward with initial velocity 112ft/sec, moves according to…

A: Topic = Algebra The maximum height reached by the stone is 196 ft.

Q: Consider the curve defined by the equation y=4x^3+14x. Set up an integral that represents the length…

A: Consider the given function. y=4x3+14x Now, find the derivative of the function. y'x=12x2+14 The arc…

Q: The roots of Characteristic equetion of a thrrd oreler, lineor homapeneous-equation with constaut…

A: Consider homogenous differential equation with constant coefficient:…

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: Find the maximum and intlection points between X =0 and 2T tor the curve /2-s Sin X

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Q: Find the length of the arc of x2 + y2 = 64 from x = -1 to x = -3, in the second quadrant. (Solve…

A: We need to find arc length.

Q: Find the arclength of the curve y = 3x² + 5 on [0,3].

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Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 <=t<= 2pai closest to the point (3/4,…

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Q: Consider an q-curve with parameters 3 and 14. a. Determine q0.05. b. Find the q-value with area 0.01…

A: The provided information are: Number of parameters (k) = 3 Degree of freedom (df) = 14

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: The edge of a cube was found to be 30 cm with a possible error in measurement of 0.1 cm. Use…

A: Given: The edge of a cube, x=30 cm The error in measurement, ∆x=0.1 cm

Q: A hollow cylinder has a radius R of the outer surface, radius r of the inner surface and height h.…

A: Given, a hollow cylinder has a radius (R) of the outer surface, radius(r) of the inner surface and…

Q: Find the intersection area between r = 3sine and T = 2 - sine curves.

A: given, r=3sinθ  and r=2-sinθ

Q: dy Use the method of isoclines to draw several solution curves for the equation dr

A: First integrate the function using variable separation method and find y as function of x  Then draw…

Q: 2. Set up the formulation to find the surface generated when the curve y=x is revolved about the…

A: Let f(x) be a nonnegative smooth function over the integral [a,b]. Then the surface area of the…

Q: What is the isogonal trajectories family of curves x² - y² = a which intersects at an angle of ∅ =…

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Q: Compute the point of intersection of the curve sinx and x-1 with the help of Bisection method. Ans.…

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

Q: Find the area in the first quadrant bounded by the curve Y = 4–?^2 and the axes using horizontal…

A: Consider the region bounded by the the curve and the axes in the first quadrant

Q: integral from -1 to 1 of arccos (y) dy

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Q: express the length of the curve as an integral but do not evaluate it. r = sin3 θ, 0≤ θ ≤ 2π

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Q: Evaluate This Integral if curve C consists of curve C₁ which is a parabola y=x² from point (0,0) to…

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Q: 5, find dt when r = 3. dt Let A be the area of a circle with radius r. If %3D %3D

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

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Q: Find the indefinite integral. Solution in handwritten. 1. secy (tany - sec y ) dy

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Q: What is the moment of inertia of this area about the line y = -10 ?

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Q: Find the equation of the tangent line to the curve y = et at the point (0, 1). Give your answer in…

A: Given,            The curve is y=exx2+1 and the point is 0,1.To find : Find the equation of the…

Q: For rigid-body motion, the strains will vanish. Under these conditions, integrate the strain…

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Q: Regionenclused by the_curve (r=2 cos20)-

A: Given:     r=2cos2θ

Q: Set up an integral to find the arc length of the curve defined by  x = tany  on the intergral 0 ≤ y…

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Q: Calculate the curve integral ∫c ( 3x2 - 3yz + 2xz )dx + ( 3y2 - 3xz +z2 )dy + ( 3z2 - 3xy + x2 +2yz…

A: Using green's theorem to find the line integral.

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

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Q: The graphs of y = srqt(x) and y = 3 - x2 intersect at one point x = r. Use Newton’s method to…

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Q: Find the equation for the principal curvatures, the differential equation of the lines of curvature,…

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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: Find the Surface avea Gevereatel by vevoluing the curve y-2r coso about te x-axis X-Sine

A: According to the given information, it is required to find the surface area generated by revolving…

Q: dx 1+e2*

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Q: Integrate h(x, y) = (x+y)i+-x)j over the closed curve that begins at (-1, 0). goes along the x-axis…

A: Let me tell you , In this problem we are going to use Green's theorem. Note: Green's theorem is only…

Q: 5. Find the moment of inertia of a plate covering the first-quad rant region bounded by y2- x, x-:…

A: Plot the given conditions for finding the boundary limits.

Q: Consider the curve defined by the equation y = 5x + 3x. Set up an integral that represents the…

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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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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.