Consider the curve r = √[1+sin(θ)], where 0 ≤ θ ≤ 2π. (a) Compute the area enclosed by the graph of the curve. (b) Set up, but do not evaluate, the integral for the length of the curve.

Q: 6. Let C be the positively oriented circle centered at the origin with radius Without evaluating the…

A: We will use the principal branch of logarithm

Q: Set up a (sum of) definite integral(s) that is equal to the arc length of the portion of the curve y…

A: The length of the curve y=f(x) between the limits x=a to x=b is given by; L=∫ab1+dydx2dx

Q: Write an integral for the area of the surface generated by revolving the curve y = cos(4x) about the…

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Q: Set up, but do not evaluate, an integral for the length of the curve. y = 6 cos x, Osxs 27 dx

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Q: Use a double integral to find the area of the region. The region within both of the circles r = 6…

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Q: Determine a definite integral that represents the area of the region enclosed by r = 7 sin 0 . de…

A: Given:                     r = 7sinθ

Q: Consider the function f(x) = (1/4) ex + e−x . Compare the definite integral of f on the interval [a,…

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Q: Use Green’s Theorem to evaluate  ∫ sin 5y dx + 5x dy  around the boundary curve C of the region R,…

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Q: Evaluate the line integral, where C is the given curve. [x² x sin(y) ds, C is the line segment from…

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Q: Convert the line integral to an ordinary integral with respect to the parameter and evaluate it.…

A: Given: ∫Cy-zds C is the helix 4cost, 4sint, t , for 0≤t≤2π. Simplifying it: ∫Cy-zdsrt=4cost,4sint,…

Q: Set up, but do not evaluate, an integral for the length of the curve, L. y=cos(x), 0 less then or…

A: Given that,

Q: Evaluate the line integral, where C is the given curve. |x sin(y) ds, C is the line segment from (0,…

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Q: Evaluate the integral (+ 2) dz where C is the line segment from the origin to the point 1+ 2i.

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Q: The area under the curve parametrized by x(t) = e", y(t) = 2et +1, where 0 St<1/3, is equal to.

A: As given, x(t) = e3t  y(t) = 2e3t + 1 where 0≤t≤13.

Q: Evaluate the integral and interpret it as the area of a region. T/2 14 sin(x) – 4 cos(2x)| dx

A: We have to

Q: Find the area of the surface formed by revolving the graph of f(x) = x3 on the interval [0, 1] about…

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Q: Use the Fundamental Theorem of Line Integrals to calculate ∫c F*dr exactly, if F= x^(2/5)i…

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Q: Evaluate the definite integral dy using area formulas from plane geometry: (2.x + 3)dr

A: the given definite integral is: ∫-222x+3 dx we have to evaluate the definite integral by using the…

Q: Find the area enclosed by the curve r V6(1 – sin®). %3D

A: First we will plot the curve and and using Double integration we will find area bounded

Q: Use a double integral to find the area of the region. The region within both of the circles  r = 4…

A: Find the intersection of the given circles as follows.

Q: 2.1 Find the tangent line to r = 0 – cos(0) at 0 = 2.2 Set up, but do not evaluate, an integral that…

A: (2.1) The given curve is -  r = θ - cos(θ).......(1) at θ = π/2 put θ = π/2 in equation (1) we get,…

Q: Set up an integral that represents the arc length of the function y = 4a4 + 5x from the point (0,0)…

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Q: Evaluate the integral and interpret it as the area of a region. •T/2 14 sin(x) – 4 cos(2x)| dx

A: Given that integral ∫0π24sin(x)-4cos(2x)dx First, we have to split integral because,…

Q: Evaluate the line integral, where C is the given curve. ∫(with c in subscript) x sin y ds, C is the…

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Q: Set up, but do not evaluate, an integral for the length of the curve. x = 8 sin(y), 0 sys. 2

A: Given query is to setup the integral for the length of the curve.

Q: Let R be the region below enclosed by the curves r = 2 - y², y = − sin (7₂2), and x = -1, as shown…

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Q: Write and evaluate the definite integral that represents the area of the surface generated by…

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Q: Let R be the region below enclosed by the curves x = 2-y², y = − sin (77), and x = −1, as shown…

A: Given: y=-sinπ2x To find: Area of R using vertical rectangles

Q: Evaluate the integral a sin y ds where C is the line segment from (0, 3) to (4,6),

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Q: Set up an integral that represents the arc length of the function g(x) = sin x for the interval [0,…

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Q: Use the property to estimate the best possible bounds of the integral. II 4 sin*(x + y) dA, Tis the…

A: Consider the given integral: ∫∫T4sin4x+ydA T is a triangle enclosed by lines y =0, y = 2x and x =3.…

Q: Convert the line integral to an ordinary integral with respect to the parameter and evaluate it.…

A: here we will convert the whole integral into t

Q: Q₂: Find the area of the region insid the circle v=1 and the Curve r= 2 sin@ (use double integral)

A: Given r=1 and  r=2 sinθ The formula to calculate the area of the region inside the circle is:…

Q: Which ONE of the following integrals correctly represents the area of the surface of revolution…

A: giveny=ln(x5)rotation about x-axisA=∫152πyds

Q: Calculate the area between the curves r2 16 sin 20 and p2 16 cos 20 .Show by drawing. %3D %3D

A: We will draw region first, then find the area using double integral

Q: D. Set-up the definite integral that will give the area of the surface generated by revolving the…

A: D) Given arc is y=2x⋯⋯(1)   Arc revolving from x=0 to x=2. a) To find: area of the surface revolving…

Q: Use an appropriate change of variable to evaluate the double integral: co where R is in the first…

A: Given the region:

Q: 1. Do both parts a) and b). a) Set up but do not evaluate an integral to find the arc length of the…

A: Solve the following

Q: Set up, but do not evaluate, an integral for the length of the curve. y = x – 9 In(x), 1sxs 4 dx

A: The integral for the length of the curve is  L=∫ab1+dydx2dx

Q: Express the length L of the curve r = sin3(0), 0 < e < as an integral but do not evaluate it. /7 de

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Q: Is the integral / A · dr path independent if A = (2x - y)i+ (x + y)j? of Evaluate A · dr around a…

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Q: The area of the region enclosed by a nonnegative polar curve r = f(0) (a <o< B) and the lines 0 = a…

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Q: Find the area under the curve y = sin 2t from t = 0 to t = π/4.

A: We have to find the area under the curve of a function y=sin2t , here we have the limit from 0 to…

Q: Evaluate the integral. (Use C for the constant of integration.) sin(t) dt os°(t) coS

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Q: Evaluate the integral by making an appropriate change of variables. 7 Cos (3 (V=X)) d y + x 637 6…

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Q: Jy Find the area of the inner loop of the curve r = 9 cos 0 - 4 by using double integral.

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Q: Evaluate the line integral, where C is the given curve. x sin(y) ds, C is the line segment from (0,…

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