Use differentiation to determine whether the integral formula is correct. 7) [(5x + 7)4 dx = 5x + 7}5 + C 25 A) No B) Yes 8) [: x2 -sin x + C X COS x dx =- A) Yes B) No
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A: A detailed solution is given below.
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- Solve using integrable combination technique only: (x^2y^3−(6+1)y)dx+(x^3y^2+(9+1)x)dy=0Revolve about the line x= -1, use disk method. (Bound by y=x4, x=0, and y=16. Mark axis of rotation, draw appropriate differential elements on a graph, and lable all the appropriate dimensions and features.)2. Verify using the Integration (preferably integration by parts if possible) Techniques each of the equality
- Find the firsst derivative of y = arctan [ (3 sin x) / (4 + 5 cos x) ] and the first partial derivative fx, fy, and fz of (x + yw )2 – ez – 2 = 0 and f ( x , y, z ) = 2xyz + tan x + y sin z Make the solution detailed and clear IN A PAPER.A basketball player makes a successful shot from the free throw line. Suppose that the path of the ball from the moment of release to the moment it enters the hoop is described by y = 2.15 + 2.09x −0.41x2,0 ≤ x ≤ 4.6 where x is the horizontal distance (in meters) from the point of release, and y is the vertical distance (in meters) above the floor. Use a CAS or a scientific calculator with a numerical integration capability to approximate the distance the ball travels from the moment it is released to the moment it enters the hoop. Round your answer to two decimal places.integral of sec^3 x