No. of integral points lying inside the parabola y² = 8x and circle x? + y? = 16 are %3D (A) 15 (B) 17 (C) 19 (D) 12

Q: O Calculate the integral y dydx

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

Q: 3. Find the area of the surface generated from revolving the curve y = x ++4 from x = 1 to x = 2…

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Q: B- Evaluate the integral 1-x (3-x-y dz dy dx /1-x²

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Q: Calculate (x²+y²) dx dy area when D is the limited to x²-y²=1, x²-y²= 9, xy = 2, xy=4

A: As per the question we are given a double integral over the 2d region D bounded by the following…

Q: Evaluate the integral / (12x + 3y)dæ + (3x – y)dy along the parabolic arc y = x² from (0, 0) to (1,…

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Q: Evaluate the integral (2x – y) dx + (x + 3y) dy along the path C. C: x-axis from (0, 0) to (0, -3)…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)2=2y, the…

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Q: The area of the surface formed by revolving the graph of x = /ỹ on [2,9] about the x-axis is given…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5) 2=2y, t at…

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Q: Use (a) the Trapezoidal Rule integral 1to 4    cos  2  x dx                 with n= 8

A: Given Data The integral is . The number of intervals is n=8.   The function of the given integral…

Q: 3. (8.3) find the area of the surface obtained by rotating the curve y = v4- x2, -1<x < I about the…

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Q: 8. At what point of the parabola is the tangent line parallel to 7x+y-2=0? y = 2r-3x +1 O (1,0) O…

A: Here is the solution:

Q: The vahe of the integral fx*dx with step length 0.5 using Trapezoidal's nule is a) 0.375 b) 0.875 c)…

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Q: 7. Find the area of the surfaces generated by revolving the curve r = 2e®² for 0<0s- about x- axis.

A: The solution are next step..

Q: The surface area of the surface generated by revolving y= 1 – x² for 0<x<1 about the x – axis is s=…

A: The solution is as follows

Q: Evaluate: ∬ 〖4X d A〗 over the region R bounded by the parabola Y = X ^ 2 and the line X = Y-2.

A: Plotting the Curves on X and Y-axis : y = x2 ...............(1)y = x + 2 ..............(2)After…

Q: 1.a) Apply the Trapezoid and Corrected Trapezoid Rule, with h=; , to approximate the integrale-2x²…

A: Note:- As per our guidelines, we can answer the first part only as both are different and first part…

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)²=2y, the…

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Q: 6. Find the area of the surface generated by revolving the curve y = x² + 2 from x = 1 to x = 2…

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Q: Find the exact value of | (yi+ vxj) · dr where C is the parabola y = x² from the origin to the point…

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Q: The numerical value of f3dA 3dA (where D is the region bounded by lines y=0 and x= 1 and the…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2 = 2y, the…

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Q: raluate the double integral : (x + 2y – 2) dy da

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)2=2y, the…

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Q: 3. Find the area of the surface generated from revolving the curve y =x++ 4 from x 1 to x 2 about…

A: Given, Curve ,y=x33+14x+4 To find : Area of surface generated after revolving the given curve from…

Q: 6) Find the length of the arc of the curve y² =x ³ from (1, 1) to (2, 2 v2) twice using two…

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Q: Suppose that the curve y =( x^4)/8 + 1/(4x^2) on the interval [1, 2] was revolved about the x-axis.…

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Q: 2.7 Describe cll soilutions of Asso where A is the Yow ta the matirix meg Vse Y S, and/or t as in…

A: Given  A=1-6-50-2-100100-200001-7000000 Here, we have to solve Ax=0

Q: y? = 1? Which of the following integrals represents the length of the upper half of the ellipse 25…

A: Topic = Application of integration  Correct answer = A

Q: Use Green's Theorem to calculate 4. [(x² – xy) dx + (y² - 2xy) dy] where C is a square with vertices…

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Q: The surface area of the surface generated by revolving y= 1-x2 for 0<x<1 about the x - axis is S = […

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Q: Find the area of the surface generated when y² = 12x is revolved about the x- axis from x = 0 to x =…

A: Given curve,y2 = 12xRevolved about x-axis from x=0 to x=3.

Q: 2.a) Apply the Trapezoid and corrected trapezoid rule, with h = 1, to approximate the integral 1 dx…

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Q: Which of the following integrals represents the length of the upper half of the ellipse = 1? 16 3…

A: we have to find the length of upper half of the ellipse

Q: Зу + 7eV X + 7ev x) dx + (10x + 7 cos(y?) ) dy C is the boundary of the region enclosed by the…

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Q: 1. Tangent to the parabola z = x + 3y?, x = 1, at point (1,2, 13

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Q: 10 The double integral 2x dædy, where T is the triangle with vertices (0,0), (3,0) and (6,3), equals

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Q: Apply trapezoidal and Simpson's rules to the integral 1 =[ \1-x² dx h=0,2

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Q: (1) Find the area of the curved surface of the upper half of the sphere x2 + y² + z² = a²(a > 0) on…

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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: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)²=2y, the…

A: Consider the circle, x2+y2=25 find the equation of the tangent line,…

Q: Calculate the double integral ∬R(x2+y2)dxdy in the circle x2+y2=2x.

A: Write the equation of circle into standard form. The radius of the circle is 1.

Q: Q2// Find the resulting volume of the curve y = sin x cos x rotation about the x-axis if x=0, x=/?

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Q: 4x Estimate the error in the quadratic approximation of f(x,y) = e sin y at the origin over the…

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Q: Y = e-5x x > 0

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Q: Evaluate the integral -5earctan(y) - dy 1+ y?

A: We have to evaluate the integral.

Q: Evaluate the integral (12x + 12y)dx + (9x-y)dy along the parabolic arc y = x from (0,0) to (1,1).…

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Q: Find the radius R, of curvature to the hyperbola y = x + 3x² – x³ at the point x = 0 given that R =…

A: To find the radius R, of curvature to the given hyperbola at point x = 0.

Q: The volume of the solid generated by the curve y = e¬ª, between x = 3 and x = 7 about the |3| x –…

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