The rate at which revenue was generated (in billions of dollars per year) for one large company can be approximated by the equation below, wheret= 10 corresponds to the year 2010. What was the total revenue generated (to the nearest billion) between the start of 2010 and 2016? f(t) = - 1.291? + + 56t – 126 10sts 16 Write a definite integral to find the total revenue generated (to the nearest billion) between the start of 2010 and 2016. dt 10 The total revenue from the start of 2010 to the start of 2016 is $ billion. (Round to the nearest integer as needed.)

Q: 5-e* 2x

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A: Given∫35f(x)dxAnd we know that the total change theorem :∫35f(x)dx=F(5) - F(3)  ---{1}

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Q: Suppose that from the beginning of 2007 to the beginning of 2017, a country consumed gasoline at a…

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A: topic- integration

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A: A detailed solution is given below

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Q: Find the indefinite integral. (Use C for the constant of integration.) 7 7 10

A: ∫ 7θ2 cos 7θ dθLet  7θ = x⇒ -7θ2 dθ = dx⇒ 7θ2 dθ = -dx

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A:

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A: please see the next step for solution

Q: Find the general indefinite integral. (Use C for the constant of integration.) - 3u4 ته( ل u? +)

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A: We need to show, how the -x2  was found in this integral? I

Q: Solve the following Integral Equation by Method of Successive Approximation:

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Q: Find the indefinite integral. (Use C for the constant of integration.) 8. xV 64 – (In x)2

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A: The rate of sales of bottled water in a country for the period 2007–2014 can be approximated by…

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Q: Suppose that from the beginning of 2007 to the beginning of 2012, a country consumed gasoline at a…

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Q: Evaluate the indefinite integral. (use C for the constant of integration.) 7r +4x2 + 6x 3 dr

A: Solved below

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) xp (x² + 5)2 х

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Q: Use the indicated formula from the integration table in Appendix C to find the indefinite integral.…

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Q: Evaluate the definite integrals using the graph of ƒ (x) below. 4- y 2- 2 4 10 12 -2- -4- -6- •4 (a)…

A: Given,

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Q: 2(x*) dx

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Q: Find the indefinite integral. (Use C for the constant of integration.) xp Vx - 4

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Q: Evaluate the following indefinite integral. Use C for any constant of integration. 4x³ + 8x² + 75x +…

A: ∫f'(x)f(x) dx = ln f(x) +C ∫xn dx =xn+1n+1+C ∫1xdx =lnx+C ∫1x2+a2 dx = 1atan-1xa+C

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Q: 1. (x² – 4x +4)x

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Q: Suppose that from the beginning of 2007 to the beginning of 2013, a country consumed gasoline at a…

A: Given: A country consumed gasoline at a rate of about q(t)=−1.1t+141 billion gallons per year and…

Q: Evaluate the following indefinite integral. Use C for any constant of integration. ' 6x³ + 2x? 20x –…

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Q: Find the indefinite integral. (Use C for the constant of integration.) 3t V9t4

A: Here, we use the formula shown on  board.

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.