5. Suppose that f(t) is the rate of snowfall t hours after midnight on December 21, measured in r12 inches per hour. What does the integral f(t) dt represent?

Q: If the change of variables u=x²+4 is used to evaluate the definite integral f(x) dx, what are the…

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Q: Find the value of the constant C for which the integral 3 3C dx x + 25 X + 5 converges. C =

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Q: 16. If r'(t) is the rate at which a water tank is filled, in liters per minute, what does the…

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Q: Find the indefinite integral. | t17 dt : +C

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Q: 2. Suppose | 29(r)dr = 10. Using linearity properties of integrals, calculate | (g(x) + 3)dx. 3

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Q: Find the linear approximation of f(x) = lnx at x = 1 and use it to estimate ln(1.02). L(x) =…

A: Given that: f(x)=lnx

Q: 1) Find dy/dt for if : y = log2 (81n 2) 2) Evaluate the following integral= In 2 log2 (x + 2) dx x +…

A: Any logarithmic function having a base other than e can b converted to a natural log as shown below:…

Q: Suppose fhas absolute minimum value m and absolute maximum value M. Between what two values must |…

A: Apply formula for finding correct option

Q: The area between the curve X= t2 - 2t+1, y= In(t) and the y-axis for 1sts5 would be found by setting…

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Q: Find the linear approximation of f(x) = ln x at 1 and use it to estimate ln(1.33). L(x) In(1.33) =

A: Given : fx = lnx

Q: valuate the indefinite integral. 7 dt (t + 1)?

A: Given query is to eveluate the integral.

Q: 8. Suppose that the net earnings of a company at time t are being generated at the rate of 25 + 5t…

A: (a) The definite integral that gives the present value of the company's earning us given as follows…

Q: 1) Find dy/dt for if : y = log2 (8r'n 2) %3D 2) Evaluate the following integral: In 2 ` log2 (x +…

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Q: Find the indefinite integral. (Use C for the constant of integration.) dt t4 + 1

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Q: How can I find the derivative of an integral. For example g(x)=the integral from 0-x (t+t^3)^.5 dt

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Q: Q16: Find the indefinite integral: (e' + tº) dt

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Q: Q3: Find the integral for the following functions: - 1 dx 1)S- Vx2-2x+1 2) S 3cotx csc² (x)dx 3)…

A: Note: Since you have posted multiple questions. We will solve the first question for you. If you…

Q: 5x+6 Consider the indefinite integral e+0 dx:

A: given equation= e5x+6

Q: Find the following indefinite integrals subject to the initial conditions a) y'= with y(1)=0 x²+6'

A: topic - differential equations

Q: Find Lf 0- £{[ e-axdx } by transforming e atu(t) then applying the integratiori property

A: Given :I=∫0te-axdx Laplace Transform u(t)→ℒu(t)us=∫0∞e-stu(t)dt we need to find: ℒ∫0te-axdx

Q: 1. Evaluate S(x + y)dxdy by reversing the order of integration.

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Q: If 9. 3. 6. f(x)dx = || f(x)dz + 6. what are the bounds of integration for the first integral?…

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y logy x * * -

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Q: A 1125 m³ open-top rectangular tank with a square base x m on a side and y m deep is to be built…

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Q: 13x? + 17 What is the indefinite integral of ) dx (2x+1)(x² + 4

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Q: Find the producer surplus ( only ) if for a product : p = D(x) = -3r + 40, p = S(x) = 2x + 10.…

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Q: 8. Find the value of the constant C for which the integral 11x 11C dx x* + 1 4x + 1 converges. C =…

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Q: For what value of a, b > 0 is the following integral convergent. dx . x°(1+x³)

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Q: What is the derivative of this integral?

A: We know that

Q: Find formulas for the functions represented by the integrals.

A: Find formula for the function represented by the given integral: ∫1x2 t dt

Q: Q2) A: Compute at the point (1, 0) for the function dx S(x,y) = cot 1(4x + em(sin2xy)) + sinh(3) +…

A: Given that, f(x,y)=cot-14x+elnsin 2xy+sin h(3)+log2x2 Which can be re - written as,…

Q: 5. Find the indefinite integral. A) f dx (x-3)Vx -6x+5

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Q: Q4. Find the integral of the following functions x dx (x-1)(x2+2x+1)

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Q: Q3/ Find the integral x e* dx by using trapezoidal and simpson methods with an error of no more that…

A: According to question given :Integral ∫01x ex dx by using trapezoidal and simpson 38 methods with An…

Q: 27. For what value or values of a does ах |dx 2x x² + 1 converge? Evaluate the corresponding…

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Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x+1) 3- xy + x²y 3 at x = 1

A: Here, We need to find the derivative of the given functions. To solve these questions, we need chain…

Q: Q3: Find the integral for the following functions: - dx 1)) T2-2x+1 Vx2-2x+1

A: we want to find the integral for given function

Q: se N.P.M. to estimate the root of -X = e -X for an initial of Xo =0

A: Here f(x)=e-x-x,  x0=0. We estimate the root of f(x)=0 by using N.R.M.

Q: Q4: To evaluate the integral fcos' xdx using the reduction formula of cosinc function

A:

Q: If V (t) is the amount of oil in a barrel being filled at time t, what physical quantity is…

A: Let's find.

Q: Find the net change in ve]locity over [1, 4] of an object with a(t) = 8t − t2 m/s2.

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Q: What value of x > -1 maximizes the integral / t²(3 – t)dt?

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Q: 6) Use the successive approximations method to solve the following Volterra integral equation: (x 2

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Q: Using Simpson's (1/3) rule with h = 1, evaluate the integral: 7 = f x² logx dx 3

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Q: 4) Evalvate the integral E 4 1+x² dx

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Q: 46) Estimate the minimum number of subintervals needed to approximate the integral T/2 6 sin x dx…

A: Find the minimum number of Subintervals.

Q: 1. Evaluate S Vx3 +1 dx dy by reversing the order of integration.

A: Given:

Q: 2t + 1 What is the indefinite integral of dt t3 -8t + 21t – 18

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Q: 1. Evaluate the integrals that converge: dx 2x ! dx (x2 + 5)3 b) a) 3-x - 00

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Q: Q3: Find the integral for the following functions: - -6 dx 1) L 2 x+2 2) S 3co t(x). csc²(x) dx 3)…

A: