The shaded area shown in (Figure 1) is bounded by y axis and the curve y? = (1.44 – x) m, where z is in m. Suppose that a = 1.44 m and h = 1.2 m. %3D

Q: Calculate the integral O (y – e*) dx + (3x + e') dy where L is along the curve x + y´ : = /x2 + y² -…

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Q: Find the line integral along the given path C. f(x-y)d: - y)dx, where C: x=t, y=3t+8, for 0sts6…

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Q: Find the area of the surface generated by e + e -y revolving the curve x = 2 0sys In 6 about the…

A: To find the surface area generated by revolving the curve x=ey+e-y2,0≤y≤ln6 about the x-axis. We…

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A: line integration

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Q: Show that at any point (x,y) on the curve y=bex/a ,the length of the subtangent is constant and the…

A: The given curve is y=bexa.

Q: Evaluate the line integral, where C is the given curve. (x + 8y) dx + x2 dy, C consists of line…

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Q: Consider the curve defined by the equation xy=25. Set up an integral to find the length of curve…

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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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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: 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: The area of the surface obtained by rotating the curve y = 1<xse about the line x = 32 is ** 12 (32…

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Q: Let L be the tangent line to the hyperbola xy = 1 at x = a, where a &gt; 0. Show that the area of…

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Q: Evaluate the integral [x² (y + 1) dx + = along the path ABCDA shown in figure." 21 y+z²+2 dy + xzdz…

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Q: Evaluate the line integral (xy dx + y dy), where C is the curve y = sin(x), 0 ≤ x ≤ π/2

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Q: The area of the surface obtained by rotating the curve y = 1 I+ X, 1 <xse about the line x = 28 is…

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Q: Evaluate the line integral, where C is the given curve. (x + 9y) dx + x² dy, C consists of line…

A: To evaluate the line integral, consider the curveC1 consisting of the line segment from0,0to9,1. The…

Q: Evaluate the line integral ∫Cydx+xdy along the curve y=x2 from the point O(0,0) to the point A(1,1)…

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Q: Evaluate the integral | (3x – 2 y + :)ds where C is the curve, C, and C, as shown. 3- y² + z² 2. 3…

A: Here, Curve C is equivalent to c1+c2. The point of intersections of c1 and c2 is at 0,1,0.

Q: Evaluate the line integral, where C is the given curve, (x + 9y) dx + x2 dy,  C consists of line…

A: Consider the line integral,

Q: 1. Find the area of surface that is generated by revolving the portion of the curve y = V4- r2…

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Q: Evaluate the line integral (e*y+ 2x) dx + (e* + 1) dy, where C is a smooth curve from the point (0,…

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Q: Which of the following is the surface area of the surface generated by revolving the curve y = 폴 in…

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Q: Evaluate the line integral - y² dx, where C is the square cut from the first quadrant by the lines x…

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Q: The area of the region under the curve A(x) = 2x+e between 0.5sxs2.0 with h 0.25 is estimated by the…

A: We have to use rectangular method to find area of the function A(x) = 2x+ex. Let's understand the…

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √((x-x) (y -…

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Q: Calculate the integral of C being the curve given below. y= 3+x y= 3-x 6x dS C

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Q: Compute 6xy da dy, where D is bounded by the curves y = 4 – x2 and y = 2x + 4.

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Q: Find the area of the surface generated by e +e -y eY + e -y in the X= revolving the curve x= -In 3…

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Q: Calculate the integral | (2x + sin y) dx + x cos y dy 7, where L is any curve from the A(0,0) to B (…

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Q: 1. Evaluate the line integral of E = xax - y ay along the segment P₁ to P2 of the circular path as…

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Q: The area of the surface obtained by rotating the curve y = -+ X°, 1sx< e about the line x = 24 is x3…

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Q: Calculate the line integral ∫Cyxdx+dy over the curve y=lnx in the interval 1≤x≤e (Figure 4).

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Q: Evaluate the line integral, where C is the given curve. |(2y3 - Vx)dy, c is the arc of the curve y =…

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Q: Evaluate the line integral, where C is the given curve. z2 dx + x2 dy + y² dz, C is the line segment…

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Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x - y)dy for the given path. C: x =…

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Q: The area of the surface generated by rotating the curve y = 2 + e*, where 1 < x < 2, about the…

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Q: The area of the surface obtained by rotating the curve y = 1 < x s e about the line x = 24 is O 2n…

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Q: Find the area of the surface generated by eY + e -Y revolving the curve x = in the interval 2 In 5…

A: solution:-given curve x=ey+e-y2 in the interval 0≤y≤ln5revolving about the y-axisarea of a surface…

Q: Find the line integral along the given path C. Ju- |(x- y)dx, where C: x = t, y = 5t + 6, for 0 sts2…

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Q: Consider the function y (x) = 1 + ex / 2, from the point (0,2) to (4, e2). Set up the integral that…

A: Given that: y(x)=1+ex/2

Q: Find the area between the curves y=e−0.2xy=e-0.2x and y=1.6x+1y=1.6x+1 from x=0x=0 to x=4x=4.

A: Given query is to find the area under the curve

Q: Use Green's theorem to evaluate the line integral for the curve C given in the figure. [8y dx + 7x…

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Q: 4. Evaluate the double integral D where D is enclosed by the curves y = a², y = 3x.

A: First we will draw the graph for given curves from that we will find the limits of x,y as shown…

Q: Use Green's Theorem to evaluate (e" + y²) dx+ (e" +x²) dy where C is the boundary of the region…

A: we have to evaluate the following by using greens theorem

Q: (2x + y)dx + (x + 2y)dy

A: Given integral is:  where C is any curve that joins the point (1,1) with the (2,2).

Q: 3) Find the area of the surface that results from rotating the curve Y = sin X, 0<X< 1 about the X…

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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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