6. Evaluate - x4 dx by making a substitution and interpreting the resulting integral in terms of an area.

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A: To solve the following problem

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Q: t Attempt in Progress antity P is an exponential function of time t, such that P = 40 when t = 4 and…

A: for simplicity take P0=a Given  for t=4 , P=40 for t = 3 , P = 50

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A: Here is the solution

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A: The given integral,       ∫-11x+4x+3dx=743

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A: The understanding of radioactive decay is required. The explanation part is given below.

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Q: Identify u and dv for finding the integral using integration by parts. Do not integrate. In(5x) dx u…

A: We will evaluate the given integral as shown below

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Q: A general solution of the differential equation - 3+4 = 0 is 1. A. y = c,e* +cze2x + c3xe²x B. y =…

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Q: Find the value of n in the following definite integral. So 4x° dx 1 Answer:

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Q: dy Find for dx 2. y = x(e*) = x(e*)

A: Given: y=xex   ....(1)   As we know that; The Product rule; f·g'=f'·g+f·g' And ddxlnx=1xddxex=ex

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Q: Suppose f(x, y, z) = x2 + y + z? and W is the solid cylinder with height 7 and base radius 3 that is…

A: Given that f(x,y,z) = x2+y2+z2 and W is the solid cylinder with height 7 and base radius 3 that is…

Q: What theorem is used to solve for centroid? Pappus O varignon's O Castiglliano's O Pascal's

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Q: Perform the indicated multiplication on the differential operator D. Show your full solution.

A: We have to find out

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Q: x+dx 1.

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Q: nd the indefinite integral using integration by parts with the given choices of u and dv. (Use C for…

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Q: Evaluate the line integral -ydx+ xdy along the curve C :y = 12x from (12, 12) to (0,0). NOTE: Enter…

A: In this question , we can find the given line integral.

Q: Find the partial derivatives of f (x, y) = 5x°y². %3D (a) fa(x,y) = (b) fy(x, y) (c) fa(3, y) = %3D

A: ∂xn∂x=nxn-1

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Q: Evaluate F. dr. Jc F(x, y) = 9xi + 6yj C: r(t) = ti + V4 - tj, -1 sts 1

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim t→+o\ 9t2 + 10' 3t (?, ?)

A: We have to find the limit

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y2…

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Q: Evaluate: /x*V1-x*dx A None 3 글(1-x4) 2 +C В 3 -(1-*) C 3 (D (1-x+) +c - C 3 은(1-x) 2+C

A: We have to solve above question and find integral

Q: Set up the definite integral required to find the area of the region between the graph of y = a? –…

A: Here we have to setup the definite integral required to find the area of the region between the…

Q: 2. Use the definition of integral to evaluate the integral (x³ + 1)dx. (hint: [ S(x)dx = lim Ës(x,…

A: A detailed solution is given below

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Q: 1. The number of arbitrary constants in a particular solution of a fourth order differential…

A: 1. We know that the number of constants in the general solution of a differential equation of order…

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A: Topic:- derivatives

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Q: Which integral corresponds to the area of the shaded region? The parabola is y = x? –1 while the…

A: Given query is to find the the integral for the area of shaded region.

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Q: Find the partial derivatives of f(x, y) = 5x°y². %3D (g) fz(1,2) (h) fy(1,2) =

A: