Provide a general solution of the ODE: (d^2)*x/d*(t^2) + 7* (dx/dx) + 2*x = 0

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A: Suppose that the radius of circular pattern is “r” and area of the pattern is “A” then, The area of…

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A: In the given question we have to find the integration by putting in the integral. So we will…

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A: How much work is required to pump all the water from a right circular cylindrical tank that is 8…

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Q: A 13 foot ladder leaning against a wall is pulled away from the wall at a constant rate of 3ft/s and…

A: Given,         A 13-foot ladder leaning against a wall is pulled away from the wall at a constant…

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Q: Use integration by parts to verify the reduction formula.

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Q: 5. 12 sec² (3x) dx 0.

A: We have to solve

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Q: A barge takes 3 hours to move (at a constant rate) downstream for 21 miles, helped by a current of 2…

A: To solve the following problem

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A: Let the length be: l Let the width be: w

Q: Integrate tan -1 x dx without using integration by parts.

A: We will find the solution in the following step.

Q: A light is hung 6 meters above a straight horizontal path. If a man 2 meters tall is walking toward…

A: Decreasing:- We know that if something is decreasing then it is going down.

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A: Follow the procedure given below.

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A: radius of a circle increases by 3%,

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Q: A rectangle's length is increasing at the rate of 5 inches/sec, its width at 2 inches/sec. At what…

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Q: find the integration of 1/(sinx*√(sin(2x))) .dx

A: Let's find.

Q: Use an appropriate substitution to integrate 12 x*(x++ 1)°dx

A: The given integral is 12x3(x4+1)9.

Q: Use differentials to approximate the change in the area of a square if the length of its side…

A: Area of a square with a side length of x cm is, Ax=x2 Here, x=5 cm & ∆x=5.32-5=0.32 cm Now…

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Q: The integration of cosx is

A: Recall: Definition of Integration:      In mathematics , Integration is a technique to finding a…

Q: Car B starts 30 miles directly east of car A and begins moving west at 90 mph. At the same moment…

A: We construct a triangle as shown below.

Q: Integrate (three) of th 1) f sin6x cos3x dx 4) [x² (1+¹)4 dx

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Q: An LRT train 6 meters above the ground crosses a street at a speed of 9 m/sec, at the instant that a…

A: Given: An LRT train 6 meters above the ground crosses a street at a speed of 9 m/sec, at the instant…

Q: Exercises to solve: 1. fx² In(x + 1) dx 2. (x2 + x – 2).cos4x. dx 3. Se-*sinxdx 4. S sinh2x.cosh5x…

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

Q: S sin4xVcos4x + 1dx

A: Let u=cos(4x)+1 Then du=(cos(4x)+1)′dx=−4sin(4x)dx  and we have that sin(4x)dx=−du4

Q: A rectangle has a length of 7 inches and a width of 8 inches, whose sides are changing. The length…

A: Given: A rectangle has a length of 7 inches and a width of 8 inches, whose sides are changing.The…

Q: he surface area of a cube is increasing at a rate of 122.2 cm2/s. At what rate is the side length of…

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Q: integrate x^4cotx^5 dx from 0.4 to 0.8

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Q: Integrate ing with res pect to x; +8 - (3x+2) - the followi Sin (x) + + 2 4x dx 4 5x

A: Formula : 1. ∫xndx=xn+1n+1, n≠12.∫(ax+b)ndx=(ax+b)n+1a(n+1)3.∫1xdx=lnx4.∫sinx…

Q: Integrate: Jez sin(3x) dx

A: Solve the integration by substitution method

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A: Given that: ∫3t2lntdt

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Q: Evaluate 4 dx V4-x2

A: To find out the integration.

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Q: When a metal plate is heated, it expands. If the shape of the plate is circular and its radius is…

A: When a metal plate is heated, it expands. If the shape of the plate is circular and its radius is…

Q: Integrate completely

A: Given,             ∫2x+12x-53dx

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Q: A 3-meter long steel pipe has its upper end leaning against a vertical wall and lower end on a level…

A: Given that, Length of pipe is 8m, lower end moving away at the rate of 2 cm/sec. we have to find how…