V'(t) = 50,000 e-3t 0sts 15 where V(t) is the value of the piece after t tyears %3D What is the change in the value of the painting in the fith year? (Gain or loss?) Write your answer in complet sentence with appropriate units Calculators are allowed to perform the integrals for this problem but you must write the integrals you are calculating

Q: [x√1 + x² dx Find the integration in the Simpsons method when n=3 Then compare the integral with the…

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Q: 5. In the real world there are many situations in which some quantity depends on a variable which at…

A: We have given  Radius r(t) = 3t  Area A(r) = πr2  Find the area  1) when t= 2 minutes  2) when t= 5…

Q: r(x) = {1.705(6.84145 l0.11879x – 3.5857 when 20 < x s 29 when 0 3 XS 20 where r was measured in…

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Q: 5. DETAILS LARCALC11M 5.2.028. Find the indefinite integral. (Remember to use absolute values where…

A: Reducing the given expression to partial fractions

Q: 6. An oil tanker struck an iceberg and is losing oil and producing a circular oil slick that is…

A: We will find the area after 16 hours by integrating the given rate from 0 to 16 Assume  Then we…

Q: 7. Water leaks out of a tank through a square hole with 1-inch sides. At time t (in seconds) the…

A: Given that water leaks out of  a tank through a square hole with 1 inches side. At time t the…

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Q: se differentials to approximate the change in revenue corresponding to an increase in sales (or…

A: Given, R=48x-1.5x2                     X=15

Q: Find the indefinite integral. (Note: Solve by the simplest method-not all require integration by…

A: Integrate the given integrand  e4xx/(4x+1)2

Q: p.1.035. MỸ NOTES ASK YOUR TEACHER Find the indefinite integral and check the result by…

A: To find the indefinite integral and check the result by differentiation.

Q: dx (x – 1)(x2 + 4)

A: SOLUTION-

Q: Tutorial Exercise Evaluate the indefinite integral. Ter V16 + eř dx Step 1 We must decide what to…

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Q: Evaluate the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

A: The given indefinite integral is: I=∫dx4x+3   ...1   As we know the common integral. ∫1xdx=lnx+C

Q: 6. Use integration by parts to find the following indefinite integral. S In(t) Jī dt You must show…

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Q: Find the general indefinite integral. (Use C for the constant of integration.) 9. 5x2 + 6 + x2 + 1…

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Q: Solution for #2: Set up(and do not evaluate) a (sum of) definite integral(s) equal to the length of…

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Q: Pumping Liquids From a Container An engineer, for example, may want know how much work is required…

A: we can solve this question with the help of integral  we took an element  of thickness dy in the…

Q: Be sure to show all definite integrals. The graph provided shows the velocity of a particle moving…

A: The velocity of a particle moving on the x-axis. The particle starts at X=-5 when t=0.

Q: Use a change of variables or the accompanying table to evalúate the following indefinite integral.…

A: Given : ∫112x-6dx

Q: Use Integration by parts to solve the following integrals. Show all your work, including the steps…

A: The given integral is ∫3-tcost dt. Evaluate the integral using integration by parts as follows. Let…

Q: Write the definite integral for finding the indicated surface area. Then use the integration…

A: To evaluate the integral

Q: 10) Depreciation: The rate of depreciation of a building is given by D'(t)=3,000(20 –1) dollars per…

A: 10.

Q: A water storage container starts leaking at time t = 0 minutes. The water leaks out from the…

A: The water leaking as a function of time is given ft=10e-0.1t If leakage starts at t =0 Then in water…

Q: The ground crew is filling the fuel tanks. You know they fill the tanks at a rate of r=100et, where…

A: Consider the given mathematical model, r=100et where r is the rate of filling of fuel in the tank.…

Q: your simpest form. factore. S dy (ay+ 13) Jyt4

A: the integration of the integral is 5/[(2y+12)(sqrt(y+4))].

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Q: The rate of U.S. per capita sales of bottled water for the period 2007-2014 could be approximated by…

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Q: Filters were installed to clean up air-born pollutants in a large office building. Suppose that at…

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Q: 7. DETAILS LARCALC11M 8.4.023. MY NOTES ASK YOUR TEACHER Find the indefinite integral. (Remember to…

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Q: Find the indefinite integral. (Note: Solve by the simplest method–not all require integration by…

A: Given,          ∫tlnt+5dt

Q: (a)  The volume (growth) of the tumor can be found by integrating the function g (t) with respect to…

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Q: A spherical balloon is inflating with helium at a rate of 320x min How fast is the balloon's radius…

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A: We use integration by parts to solve this integration but first use substitution method

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Q: 1. A child lets go of a helium-filled balloon from a height of 4 feet above ground. The value of…

A: Explanation: The initial height is 4 feet above the ground. The rate of change of height has to be…

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Q: Subject: Integration by parts Evaluate the integral from 0 to 1 of (x^2+6)e^-xdx I am getting…

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Q: Pollution from a factory is entering a lake. The rate of concentration of the pollutant at time t is…

A: Given:Here P'(t)=175 t12 , where t is the number of yearsTo find:we have to find…

Q: Oil is leaking out of a tank at a rate of R(t) gallons/hour, where t is me are 10 gallons of oil in…

A: a) The definite integral that represents the total amount of oil that leaks out in the first two…

Q: or evaluate the integral by com xp 32 4x

A: The given integral is ∫x32+4x2-x4dx

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Q: (a) In one or two sentences, write down an interpretation of the definite integral 10 | (B(t) –…

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Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A: I=∫axx2-pxdxI=∫axx(x-p)dxI=∫ax-pdx

Q: A water storage container starts leaking at time t = 0 minutes. The water leaks out from the…

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Q: The integral below represents the area of either a triangle or part of a circle, and the variable of…

A: Given : an integral∫-9981-x2dx Formula: ∫ a2-x2 dx =x2a2-x2+a22 sin-1…

Q: c'(x) = 5x – 2 ; 10 units cost $66.85 Write the integral that is necessary to solve the problem. 5x…

A: Cost function = integral of Marginal cost function.

Q: The rate of growth of a population (in millions per year) in the year x is approximated by f(x) = xe…

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Q: The rate of growth of a population (in millions per year) in the year x is approximated by (x) = xe…

A: The rate of growth of population is given by  f(x) = xe-x^2 Population in second year = 60000

Q: Find the indefinite integral. (Note: Solve by the simplest method-not all require integration by…

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Q: (iii) The volume of air, V mL , in a spherical balloon at time t seconds, is decreasing dV at a rate…

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.