1. A hot metal object is submerged in cold water. The rate at which the object cools (in degrees per minute) is a function f (t) of time. Which quantity is represented by the integral f(t) dt?

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: 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: Match the integrals from negative infinity to time twith their corresponding functions that are zero…

A: Given graph of the functions 1. 2.

Q: (b) / e*+e* dx.

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Q: That the value of the integration g(1) = 0, g(2) = 0 1-e) -dt where g is a function that is…

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Q: The value of the definite integral' f(x )dx for f(x) = 3 is:

A: We are going to evaluate the value of the given definite integral for f(x)=3

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

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Q: 2. Given that is a positive constant, consider the following function: f(x) = 3000 r-4, x > 10 (a)…

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Q: find the absolute extrema of thefunction on the closed interval. y=x^{2}-8 \ln x,[1,5]

A: Given:- function y=x2-8 Inxdefined on the interval 1, 5 The derivative of the function is y'=2x-8x…

Q: Find the indefinite integral.

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Q: Find the indefinite integral. -0.02t dt = +C

A: It is given to find out the indefinite integral of f(x)=e-0.02t We know that ∫exdx=ex

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: Find a formula for the function represented by the integral 3t dt

A: Please refer to the image below.

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

A: Given query is to eveluate the integral.

Q: Find the indefinite integral. 3 8 dt = t3 t2 +C

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Q: 5. Suppose that f(t) is the rate of snowfall t hours after midnight on December 21, measured in r12…

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Q: 2. Find the interval [a, b] for which the value of the integral (2 + x − x²) dx is a maximum.

A: ∫ab(2 + x -x2 )dx here for get maximum value we have to differentiate the function  so here first…

Q: Evaluate the integral. (x² + 2)e¬× dx

A: To evaluate:∫01x2+2e-xdx

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: Find the indefinite integral. t2 dt 3= t3 +C

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

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Q: In the following equation/s, find the indefinite integral :-

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Q: e*dx e -x +1

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

A: topic - differential equations

Q: 1. Use formal substitution to find the indefinite integral (a). de f(-6a) (r-3) de (b)

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Q: -2t +8 What is the value of the definite integral dt? Enter your answer as an exact fraction if…

A: The given integral is ∫19-2t+8tdt. Evaluate as follows.

Q: Find the indefinite integral. ∫(e1t/t2) dt

A: Given: I=∫e1tt2dt for evaluating given integral, in given integral we substitute  1t=p…

Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate ln(1.34). L(x) =…

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Q: dx Q24: Find the integral of f (x+1)(x2+1)

A: The given integral is ∫1x+1x2+1dx.

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

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Q: Find the indefinite integral ∫ t/√(1 − t4) dt

A: Given integral, ∫t1-t4 dt

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

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Q: e2x 2.) S. dx ex – 5

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Q: 15 Find the integral | 2/x (1+x) dx.

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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: Evaluate the definite integral on the interval [1,2] (e^1/x ) / x^2 dx

A: Given that a function f(x) and we find its integration between 1 to 2 . Here i attached solution of…

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

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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 the indefinite integrals: x5/2 + 4x +1 a) / 2 + Te' ) dt t3 6t +

A: We know that ∫xn dx = xn+1n+1+C         n≠-1 ∫1x dx = lnx+C

Q: Find the indefinite integral. Solution in handwritten b. f(x+1)√2- xdx

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Q: Suppose F(x) = 19 dt. Find a formula for the function F(x4) expressed using an integral. e F(a*) = /

A: The given integral is F(x)=∫19xe-t2 dt

Q: i +j- t3/2 k ) dt |

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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…

A: topic- derivative and integral

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

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Q: dy y(y²+1)

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Q: Find the indefinite integral: (t3/2 + t-1/2 - 10t-1) dt

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Q: 1 and use it to estimate In(1.26). Find the linear approximation of f(x) = ln x at x L(x) = In(1.26)…

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

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