Consider the integral given by (3+ 3z) dæ Using the following definition of the integral | f(z)dz = lim f(x;)A¤ %3D n00 i=1 where x; are right hand endpoins. (a) Determine Ax and r;. %3D (b) Using the definition mentioned above, evaluate the integral. Value of integral:

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A: Solve the following

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Q: Use the limit definition of definite integral in the form of f(æ) dæ = lim {(#:)Ax, i=1 6 - a and r;…

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Q: Consider the functions given.evaluate the integrals

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A: Given,f(x)=2x when x≤1f(x)=2 when x>1a)∫01f(x)dx=∫012xdx;                       (here limit of…

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Q: Set up the integral to find the length of the curve f(x) = V1 – 2? for 1/v2 <x < 1.

A: Please see the answer below.

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Q: 39. Use the definition of the integral to find the exact answer to x*dx , that is find lim f(x, )Ax.

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Q: The integral from a to b of f(x) is denoted by_____

A: Given, To fill the blank The integral from a to b of f(x) is denoted by_____

Q: Define the following improper integrals integral - infinity to 0  f(x) dx

A: Given: The improper integrals f(x)dx from limit -infinity to zero.

Q: Consider the integral given by | (2 – a?) da - Using the following definition of the integral n…

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A: Given that : The equation of the curve is y = x2 + 1 .

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Q: Which of the following statements about integrals is true? A Scsc(x)dx= cot(x) + C csc(x)dx =…

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Q: Which of the following is incorrect about the properties of an integral? rx)dx = - L, f(x)dx Si…

A: As we know that from property of definite integration.

Q: So (x²+3x+3) dx Theorem 4% f6) dx= lim f (xi) Ax where Ax= b-a and x= atcAX

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A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

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Q: 2. Use the definition of integral to evaluate the integral (x³ + 1)dx. (hint: [ S(x)dx = lim Ës(x,…

A: A detailed solution is given below

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A: Given. ∫09f(x) dx=20 To determine. ∫03xf(x2)dx Let x2=u Differentiate the function x2=u.…

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral 13 In(x)…

A: (1) The trapezoidal rule gives: So, T12≈2.0810

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A: Given integral ∫1221-1x2dxwe have to evaluate the given integral using the fundamental therorem of…

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Q: 2. In each part, use a definite integral to find the area under the curve y= f(x) over the stated…

A: We have to find the area of the given functions over the given interval using definite integral.

Q: Suppose we want to find the area enclosed by the curves y1 (z) = sin(z) and y2(z) cos(z) %3D %3D to…

A: We will answer the first question since exact one was not specified. Please resubmit the question…

Q: 3) Use the definition of the integral to write n k п lim k k=1 n as an integral. Do not evaluate…

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Q: -0.1x dx e 1 8.

A: We use integration of e^x dx =e^x.

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Q: Write the limit lim no 2 이 2 2-2 da; dx; da; dx; 3-2 32 3 512 102 5 2 Aæ as a definite integral over…

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Q: Evaluate the integral (use the substitution) : 2x + 6 x2 + 6x + 13 dx а. In (x + 6x + 13) + C b. 1…

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Q: Evaluate the following integral by using the limit definition (3a +2) da

A: To calculate the integral using the limit definition.

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Q: c) Now compute the numerical value of the definite integral by determining the limit of the…

A: To evaluate ∫39 2+6x dx Using the equality ∫abfx dx =limn→∞ ∑i=1n fxi △x, where △x=b-an and xi=a+i△x