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- Calculus Define T:P2R by T(p)=01p(x)dx What is the kernel of T?laplace transform L { cos(2t) } pls use integration by partsI need some help with the question below The velocity of a particle at time t is v(t) = cos(t). Use the Fundamental Theorem of Calculus to find the total distance traveled by the particle between t= 0 and t=π/2.
- 1.Evaluate the line integral ∫CF→⋅dr→ using the Fundamental Theorem of Line Integrals if F→(x,y)=(10x+10y)i→+(10x+10y)j→and Cis the smooth curve from (−1,1)to (8,9). Enter the exact answer. ∫CF→⋅dr→(a) Find the exact area of the surface obtained by rotating the curve y = e^x about thex-axis over the interval 0 ≤ x ≤ 1.(b) Determine the length of the parametric curve given by the following set ofparametric equations.x = 3 cos t − cos 3t, y = 3 sin t − sin 3t, 0 ≤ t ≤ πYou may assume that the curve traces out exactly once for the given range of t.Fast pls solve this question correctly in 5 min pls I will give u like for sure Sini find the surface area of the part of the paraboloid z=x^2+y^2 that lies between the planes x = 1 and x = 4.
- When recording live performances, sound engineers often use a microphone with a cardioid pickup pattern because it suppresses noise from the audience. Suppose the microphone is placed 6m from the front of the stage and the boundary of the optimal pickup region is given by the given cardioid r=12+12sin(theta), where r is measured in meters and the microphone is at the pole. The musicians want to know the area they will have on the stage within the optimal pick up range of the microphone.A rod with density p(x)=4+sin(x) (in grams per cm) lies on the x-axis between x=0 and x=pi/3. Find the mass and center of mass of the rodA closed curve line integral in ℝ3 Evaluate ∫C∇(-xy + xz + yz) ⋅ dron the curve C: r(t) = ⟨sin t, cos t, sin t⟩, for 0 ≤ t ≤ 2π.
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