If fex) = tdt,use the fundamental theorem Of culculus, part 1, +o find f'cx).

Q: Find the area of the circular washer with outerradius 2 and inner radius 1, using Fubini’s Theorem

A: Given Circle with radius ‘2’  Circle with radius ‘1’

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 80,0 < 0 <…

A:

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 30,0 < 0 <…

A: Given, r=3θ,  0≤θ≤5.4

Q: State the theorem of Arc Length.

A: State the theorem of Arc Length.   The arc length is x360°2πR. here R is the radius of the arc and x…

Q: Find the favily of orthogonal trageclores %3D

A:

Q: 2. Show that an equilateral triangle can be inscribed in the epitrochoid and that its centroid is on…

A: An equilateral triangle can be inscribed in the epitrochoid and that its centroid is onthe circle of…

Q: Describe the interual(s) on which the funchion is continous. %3D XA

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Q: A-Use Simpson's Rule with n=2 subintervals, evaluate the integral - Inx. dx, and compare the…

A:

Q: Which lines or line segments or rays must be drawn or con- structed in a triangle to locate its a)…

A: (a) The orthocentre is the point where all the three altitudes of the triangle cut or intersect each…

Q: Find the formula of the area of ellipse using calculus integrals

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Q: Give a parametric description for a cylinder with radius a andheight h, including the intervals for…

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Q: A- Use Simpson's Rule with n=2 subintervals, evaluate the integral - Inx.dx, and compare the…

A: According to Simpsons rule, ∫abfxdx can be approximated to ∆x3fx0+4fx1+2fx2+4fx3+ ……

Q: Determine the arc oF the Cur Vて length 9x² = 4(y-1)' por 1s yš2: %3D

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Q: What's the probability that the point (that is chosen at random from the unit cube) lies below the…

A: The figure is as shown below:

Q: )2. Find the paramehic from the cuve check whether the cure is a repulor cuve. Alo reparzmetije the…

A: We have to find the parametric form of the curve

Q: (०हागो 10,3,0)and (0,0,6). Tongular lamina with for of stokes deo theorem.

A: Given

Q: Find -&gt; arc JK -&gt; arc NJ -&gt; arc JL

A: Please see the explanation below.

Q: The change in the relative configuration of point within a solid is called strain

A: Strain is a description of deformation in terms of relative displacement of particles in the body.

Q: Find the sccond derivate Of the finctron Y =2*. Inx

A:

Q: Exercise 7. Show that the curvature of a circle of radius r is , and the curvature of the line is…

A: Show that the curvature of a circle of radius r is 1r and the curvature of the line is zero.

Q: Show that the volume of a spherical block can be approximated by ∆V ≈ ρ2 sin ϕ ∆ρ ∆ϕ ∆θ.

A: Suppose x,y,z is a point at fixed distance from the origin in the 3D-space.

Q: . Consider point (a, b) on the graph of y = Inx and triangle ABC formed by the tangent line at (a,…

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Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r=2θ, 0≤θ≤4.5…

A: Given that  r=2θ, 0≤θ≤4.5 To Find the area enclosed by the closed curve obtained by joiningthe ends…

Q: Give an example of a plate such that its center of mass does not occur at any point on the plate.

A:

Q: please prove this using the definiton of compactness

A: To show that the given set 1n|n=1,2,3,.....∪0 is compact.

Q: Find the center of mass of solid revolution if an area in Ist Quadrant (Kuadran Pertama) bounded by…

A: Given functions are Intersection points Area of region is Centre of mass revolution

Q: the bollowing homogeneous . Solve dilferential Eq/uatlion du %3D By

A: Given:

Q: Find the arc length of the cardioid r = 2 – 2sin©.

A: Given that: r=2-2sinθ Differentiating with respect to theta,…

Q: The figure shows a steel semi-circular plate described by a region D. Assume a constant (uniform)…

A: Here is the Answer and Explanation

Q: Determine the area of the right half of the cardioid formed by r = 8 +7 sin 0 16 14 12 10 8 6 4 -2…

A: The formula to find the area is, A=∫ab12r2dθ Since it is been asked to find the area of half of the…

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 40,0 ≤ 0 ≤…

A:

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 10, 0 < 0…

A:

Q: Find the moments and center of mass for the lamina of uniform density S bounded by the graphs of the…

A: Graph the region: The values along the y-axis varies from y = 0 to y = 3.

Q: A thin plate has mass 3. What is the x-moment of the plate if its center of mass has coordinates (2,…

A:

Q: What are the coordinates of D' and C' after DC undergoes a dilation centered at point E with a scale…

A: It is given that, scale factor is, k=3. Dilation center is at 6 vertical units above the origin and…

Q: 2. By integration, show that the area of a circle of radius r is A = rr?

A: According to our guidelines, we can answer only one question or three subparts of a question. Other…

Q: Evaluate the expression for Area of the cone using appropriate “dS” from spherical coordinate…

A: For a cone with height h and radius r the semi vertical angle is θ=tan-1rh. Thus, calculate the…

Q: Find the average distance from a point inside a solid ball of radius R to the center of the ball.

A: The average value of a function fx,y,z is davg=1V∫∫∫f(x,y,z) dV. Here the function is the distance…

Q: A right cylinder of radius r is inscribed in a hollow sphere of fixed radius a. The

A: Given, a right cylinder of radius 'r', is inscribed in a hollow sphere of fixed radius 'a'. The…

Q: Find the mibimal distance between the foint Cl,4) to the linz Yeメtl. dっしくーメュ+(-

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Q: )2. Find the paramehic from the cune check whether the cure is a repulor cuwe. AGo reparametije the…

A: Note: According to our guideline we will answer the first question as the exact one is not…

Q: write the line thraugh y S.0;?) (5,0, in the dircetion of 2 vcetor parametruc امپري؟

A:

Q: What is the general process to fit random 3D points to a surface?

A: Hint: Here 3D points are given we need to plot them on a surface. Write the general process to plot…

Q: Use three-particle interaction to show that mass is an additive.

A: We have to use three-particle interaction to show that mass is an additive.

Q: Find the area of the circular sec- tor having radius 3 ft and 0 = 7.2radians %3D

A: Formula:

Q: xplain why the annulus {z: 1 |Z| 2} is not simply connected.

A: By using Cauchy's theorem G is not simply connected.

Q: Which of the followings is/are spring of constant radius? Choose all that apply.

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Q: The center of mass of a lamina of total mass 5 has coordinates (2, 1). What are the lamina’s x- and…

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Q: Find the radius of curvature of 6y = x3 at the point (2,). %3D

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Q: Prove that the kronecker delta and Levi Civita Tensox of respectiely. Symbels 2 and are rank 3.

A:

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.