As a result of COVID-19, some students attended less than H/2 hours of lectures before the college was closed down and passed the quizzes so they are qualified to take the examination.The final score each student got is proportional to the amount of lectures he/she had attended which is given by the function L(t)=(100/H)t What was the average in the class?

Q: Evaluate the definite integral. (Assume a > 0.) ra2/5 x*V a² - x5 dx

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Q: Find the formula for the function represented by the integral dt 6t+3 %3D

A: use the substitution method  for finding the integral

Q: |In (x)| dx 00 1+ x2

A: Given integral

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dt…

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Q: g+y= 쓸 - zxe - 5

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Q: In evaluating / (2x – 3) Vx– 2 dr by substitution, if 4 =x - 2 then what will be the resulting…

A: Given : Indefinite integral ∫2x-3x-2 dx   To find : Resulting indefinite integral by substituting…

Q: Obtain the integral of the following function f(x) where f(x) = 9v5+ 9. has S f(x) dx in the form…

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Q: Show that Q(i) is an integral domain

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Q: In evaluating JxVx-2 dr þy substitution, if u =x- 2 then what will be the resulting indefinite…

A: Explanation of the answer is as follows

Q: Make a substitution to express the integrand as a rational function and then evaluate the integral.…

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Q: Consider the integral -8e-2' dt If the integral is divergent, type an upper-case "D". Otherwise,…

A: Given: ∫-∞-1-8e-2tdt

Q: Exercise 3. Use the properties of definite integral in the following: a) If f f(x)dx = 12, and…

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Q: A defense contractor is starting production on a new missile control system. On the basis of data…

A: Given: L'(x) = 2,000x-12   To find: The number of labor hours required to assemble the 26th through…

Q: Find the Fourier integral formula for the following function: = { *+1, =| 7. f(r) 0,

A: We will find out the required fourier integral.

Q: Evaluate the integral of (t2) / √(1+t2 )with respect to t.

A: It is given that, f(t)=t21+t2 It is known that, ∫1(x2+a2)dx=logx+x2+a2+c and…

Q: Evaluate the definite integral (from 5 to 7)∫(d/dt (2+2t^4)^(1/2) dt using the Fundamental Theorem…

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Q: dx 2 -o x+4x+5

A: The general form of a complex number is given by , where a, b are two real numbers and . Any complex…

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

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Q: e (In z)°dæ Evaluate the Integral

A: we have to find the integration of f(x) f(x)=∫0∞ex2(ln x)2dx ∫udv=uv-∫vdu             u=(ln x)2…

Q: Find the integral. (te -7e dt

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Q: 1 4n + 3 n=1

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Q: Evaluate the integral. (11 - t)/e dt

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Q: Consider the definite integral. (8x- – 1) e*x²-x dx Let u = 4x2 - x. Use the substitution method to…

A: Answer and explanation is given below

Q: Evaluate the integral from 0 to pi: ∫cos4(2t)dt

A: ∫0πcos42t dt

Q: 1. A sprinter is running a race. If f(t) describes the sprinter's speed in meters per second, t…

A: f(t) represent sprinters speed meter per second.

Q: Evaluate dt using a trig substitution. As well, provide another solution to evaluating V4+ t2 this…

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Q: Find the Fourier integral representation of the given function. ex, Ixl 1 f(x) = 1 f(x) da %3D Jo

A: Given - fx = ex,x < 10,x > 1 To find - Find the Fourier integral representation of the given…

Q: 1+t dt 1+t²

A: I = ∫1+t1+t2 dtI = ?

Q: Estimate the double integral_R  (3xy^(2)+2x^(2)) dA where R= [0,1] x [0,1] by diving R into four…

A: We need to evaluate integral.

Q: In evaluating /(3r2-1)2 dr by substitution where =3r2-1, what will be the resulting indefinite…

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Q: Find the indefinite integral

A: Given: ∫tt4+25dt

Q: (8ti + tj – k) dt

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

A: Given integral, ∫t1-t4 dt

Q: t * et  Compute the convolution integral.

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Q: Find the indefinite integral.

A: Consider the given integral ∫2-1tt2dt

Q: Evaluate the integrals. It may be necessary to use a substitution first. ∫ t dt/t4 - t2 - 2

A: Let's obtain the partial fractions:

Q: 3x2 dr In evaluating by substitution, if u =x+1 then what will be the resulting indefinite integral…

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Q: Evaluate the definite integral. 2 St³√₁+t² dt 0

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Q: let g’(t) represent the rate of growth of a dog, in pounds per year. What then, does g(t) represent?…

A: Given: g'(t) represents the rate of growth of a dog in pounds per year.

Q: stamp collector has 3000 stamps in his collection on January 1, 2005, and is collecting more stamps…

A: Given, Number of stamps, stamp collector have on January 1, 2005 = 3000  stamps Rate of collecting…

Q: Consider the definite integral. (10x - )x – 1) ex²-x dx Let u = 5x2 – x. Use the substitution method…

A: As per our company guidelines we are supposed to do only first question. Kindly repost the other in…

Q: In evaluating /x V4-x dr by substitution, if =4-x then what will be the resulting indefinite…

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Q: Find the general indefinite integral. √ (9 -1) (4 +1²) dt

A: Solution of given question is written in below steps.

Q: Let p (x) 3x + 2 be a first degree polynomial. Compute the following integral below using…

A: We can find the integration as below

Q: Substitute u = x + 2 into u10 - zu° +c to evaluate the given integral in terms of x. 10 x(x + 2)8 dx…

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Q: Calculate the primitives of the functionf: D R, using the table of undefined integrals and their…

A: The primitive of a function is also called antiderivative of that function. To find the anti…

Q: Evaluate the given definite integral using appropriate substitution: V2rdr = ... A ... B ...

A: We have to solve the Integral

Q: and then evaluate the resulting integral to get I =

A: Use the graph to convert the integral into the polar coordinates. Then use the properties for the…

Q: Evaluate the indefinite integral. 4 -dt (t + 10)° + C

A: Given: Let I=∫4t+106 dt To Find: To evaluate the given indefinite integral.