Since YouTube first became available to the public in mid-2005, the rate at which video has been uploaded to the site can be approximated by v(t) = 1.1t2 − 2.6t + 2.3 million hours of video per year    (0 ≤ t ≤ 9), where t is time in years since June 2005.† Use a definite integral to estimate to the nearest million, the total number of hours of video uploaded from June 2010 to the June 2013.  million hours of video

Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of…

A: We need to evaluate the following integral I = ∫4+1t31t2dt                            ...........1

Q: The rate of new tree growth (in millions of cubic meters per year) in the Sudan t years after 1980…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) | (in(x))6 dx х

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Q: Find the indefinite integral. (Use C for the constant of integration.) 2t dt 1- 4t"

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.)

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Q: te-t dt.

A: To find ∫03te-tdt

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A: Given integral  ∫9x81-lnx2 dx keep in mind the formula  ∫dxa2-x2 =  sin-1xa+C

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A: Use substitution method

Q: Use substitution to find the indefinite integral.

A:

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Q: What are two options for finding the indefinite integral below? ∫ 5t dt

A: ∫5t dt First option: We can integrate it directly by using the formula ∫xn dx=xn+1n+1+C, we get ∫5t…

Q: Use an appropriate u-substitution to evaluate the indefinite integral -dt. Use C'for the constant of…

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Q: Find the indefinite integral. (Use C for the constant of integration.) 9. dx XV 81 - (In x)2 |

A: Here we will solve the given integral,

Q: Use integration by parts to evaluate the definite integral. 8t? In(t)dt Give an exact answer

A: ∫1e8t2lntdt=8·∫1et2lntdt=813t3lnt-3·∫t23dt1e=813t3lnt-3·t391e=813t3lnt-t331e=82e39+19=82e3+19

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

A: This question can be solved by using some basic formulas of integration like ∫xndx

Q: Why does Hm have minus x in front of it. How did they do integral?

A: Both the questions are explained in step 2.

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) [ (In(x))²6 dx X

A: topic- indefinite integral

Q: Find the Indefinite Integral by making a change of varlab of Integration.) dx

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A: Given vt=1.1t2-2.6t+2.3    0≤t≤9

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Q: Find the indefinite integral. (Use C for the constant of integration.) t° Vt9 - 23 dt

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) dt

A: To find ∫ t5e-t6dt

Q: Evaluate the indefinite integral. (Use Cc for the constant of integration.) |

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Q: | Suppose that the net earnings of a particular company at time t are being generated at the rate of…

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Q: Evaluate the indefinite integral. (Use C for the constant of integra 9 dx 8V1- x2

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Q: Find the indefinite integral by making a change of variables. (Use C for the constant of…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) dx 1 + x20

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Q: Find the following integrals. Do not add any constants of integration, as the resulting functions…

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Q: Find the indefinite integral. (Use c for the constant of integration.) [ (71- - 8tj + In(t)k) dt

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Q: Use integration by parts to evaluate the definite integral te dt.

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Q: Use the definition of the definite integral to evaluate ∫02 (3x2 +1)dx. Use a right-endpoint…

A: As a first step, let's plot the graph of the curve given to us. Let's call the curve y = f(x) = (3x2…

Q: evaluate the indefinite integral 3+ -dt. Use C for the constant of integration.

A: Given : ∫3 + 1t61t2dt

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) dr

A: Follow the procedure given below.

Q: ---) dz

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Q: Find the indefinite integral. (Use C for the constant of integration.) 7 dx 49 - (In x)2

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Q: Provide an example of an indefinite integral that when integrating requires r as a substitution. As…

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Q: Why can the constant of integration be omitted from the antiderivativewhen evaluating a definite…

A: We omit the constant of integration when evaluating a definite integral, because we subtract the…

Q: ***** Find the indefinite integral. (Use C for the constant of integration.) 15 XV 25 - (In x)

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) 8t dt 8t + 5

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Q: The approximate value of a definite integral that is obtained using the simpson's rule will always…

A: We have to find the given statement is true or false. Let us consider the example given below

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Q: 3. エーy +3 dy Y+5

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Q: Find Lebesque integral of function on segment (0,1) f(x) = if- 7h+1

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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.