4. [Geogebra Question] Let f(x) = (1 – x) In(x²)+3.0225887223. Use Geogebra to find the definite integral of f(x) on the interval [0, 4] (i.e., find :| f(x) dx). Press the = button for a numerical answer. Submit a screenshot.

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Q: =D1 || |

A: I am attaching image so that you understand each and every step.

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A: use the definition  of exact or non exact.

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Q: Direction: Solve the following equations using separation of variables. 5. y*y' + y' + x2 + 1 = 0

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Q: Find the slope of the line that is tangent to the graph of f(x)=3x²-2 at P(-3, 25). O -3/25 O 27 O…

A: As per the company's guidelines, we are supposed to solve the first question for you, kindly repost…

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Q: (b) dx (1+ x²)² 0,

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A: Given line x-38=y2=z-714=tAny point on the line is of the form,x=3+8t,y=2t,z=7+14t,Put…

Q: Find the Laplace Transform of the following functions s? – o? 1) f(t) =t cos(@t) Ans. F(s)= (s² + w*…

A: According to our guidelines, we can answer only three subparts of a question. Kindly repost the…

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Q: The graph shown below is f(x) = 2x 2 - 1. If g(x) = Sốf(t)dt , find g '(3). %3D 4 2 X 54 3 -2 - V1 2…

A: g(x)=∫0xf(t)dtThenBy fundamental theorem of integral calculusg'(x)=ddx∫0xf(t)dt=f(x)g'(x)=2x2-1

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Q: Evaluate by using homogeneous D.E. 3 (3x? + y²) dx – 2xydy = 0 O ao3 = C(9x³ + y³) O ap3 = C(9x² +…

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Q: In Exercises 5–8, choose rectangular or polar coordinates to set up an iterated integral of an…

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Q: Which of the following integrals are improper? (Select all that apply.) dr 6x – 1 dr 2r – 1 sin (x)…

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A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Direction: Solve the following equations using separation of variables. 4. sin(x)dx + ydy = 0, y(0)…

A: Given

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Q: x ys dA X² +1 R.

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Q: t3 sin 8t

A: Given problem:- t3 sin(8t)  To find:- Laplace Transformation of given function

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A: Given: y=x3+2x32x-4   As we know that; The Power law; ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x The…