Evaluate the integral. S tan (2x) sec (2x) dx .5 Find the limit

Q: Evaluate the integral as a number, ∞, or −∞ or DNE if there is no limit. Also, determine if it…

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Q: O: If the improper integral converges,Show and find its valuo or ex plain why it diverges: O. X Sin…

A: The integral will converge if it is equal to some finite fixed value.

Q: In the given equation/s as follows , explain why the integral is improper and determine whether it…

A: Definition of the improper integration helps to find the type of integration. A definite…

Q: 4. For each of the following improper integrals, note WHY it is improper, and then set up the…

A: Given: a. ∫1∞ 1x3 dxb. ∫-∞4 3x+2 dx To write: Why the given integrals are improper and to set up the…

Q: The integral I = 1 + dx is [Hint: You may need to use the Mean Value Theorem for Derivatives] O…

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Q: 2. Determine if the following integral converges or diverges. If the integral converges, find its…

A: We need to check whether the given integral converged or diverges.

Q: Determine whether the improper integral converges or diverges, and find the value of the integral if…

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Q: Evaluate the following Improper Integral. Does the limit converge? Why or why not? 1 dx xIn x

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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.

A: We are asked to evaluate the integral using definition of integral

Q: e improper integral x dx diverges lect one: O True O False

A: We have to choose the correct answer

Q: Evaluate the following improper integral if it is convergent. 00 10 dx x In x Select the correct…

A: Given information:          The integral is ∫2∞10x ln xdx  Calculation: The integral will converge…

Q: Determine if the following integral is convergent or divergent. If it is convergent find its value.…

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Q: Use series to approximate the definite integral S xcos(x²)dx . (Give your answer correct to 10-3)

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Q: Solve the following improper integral. State whether the integral converges, or diverges. If it…

A: To state whether the given improper integral converges or diverges ∫4∞1x3dx

Q: 4) For each of the improper integrals below..... • Re-write the integral using the correct limit…

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Q: 3. Determine if the following integral converges. If so, evaluate the integral. 8 dx (5 – 2x)

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Q: Refer to the image attached

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Q: Evaluate the improper integral. See if it is convergent or divergent: (1 – x)e¬# dx

A: The improper integral is ∫0∞1-xe-xdx.

Q: In the given equation/s as follows , explain why the integral is improper and determine whether it…

A: The given integral is ∫02 1x-12 dx. Note that the function fx=1x-12 is unbounded on 0, 2. Because…

Q: In the given equation/s as follows , explain why the integral is improper and determine whether it…

A: The given integral is ∫04 dxx. Note that the function fx=1x approaches infinity as the value of x…

Q: Consider the integral equation below, 3 e2 sin (e²ª)dx = Which of the following is a possible value…

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Q: Evaluate the integral as a number, ∞, or −∞ or DNE if there is no limit. Also, determine if it…

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Q: c) I following 1. Determine whether the integral is convergent or not. 10 [." : 6 dx x-6 Vx

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Q: Which of these improper integrals is convergent? e dz 1 eda e*dx 3 -dr 3 -dr 3 8 8

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Q: Consider the definite integral J 2e0" dx. 1 What is the summation that is equivalent to the definite…

A: The answer is mentioned below

Q: Evaluate the following improper integrals. Tell whether it is convergent or divergent. dx (x-1)%

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Q: State whether the following integral converges or diverges: cos x/ √ (2 − sin x) dx  limit: (0 to π/…

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Q: dx Determine if the following integral converges ? 3 – 2x

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Q: dx Use the fact (1+x)x^; dx = 2 tan" (Vx)+C. You will need to think a little on this one©. 2.…

A: We will use the given indefinite  integral to  check whether the improper  integral given converges…

Q: Note: You may need to assume the fact that lim M"e-M = O for all n. M + o Decide whether or not the…

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Q: x cos x - sin x - dx x2 x sin x dx roo dx |(x* + 1)²

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Q: +00 dx Evaluate the improper integral x(In x)²

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Q: e-a dx.

A: COMPARISON TEST

Q: dx e sin x dx 1 dx x2 + 4 -00

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Q: Q1) Evaluate the following integral: y : tanx dx

A: To solve this question, We will use the identity- 1+tan2x = sec2x

Q: 4. Use the comparison property to calculate if the following integral converge: sin? x =dx.

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Q: Which of the following definite integrals represents the limit: 1+ z?A¤ lim n00 You may use the fact…

A: Given:-limn→∞ ∑i=0nxi1+(xi)3 ∆x    on the interval 2, 5integral as limit of sum∫abf(x)dx=limn→∞…

Q: (b) For each of the following improper integrals, use the Comparison Test to justify whether it…

A: According to question given that (i)  ∫1∞1+sin2xxdx     (ii) ∫1∞x+1x4-xdx

Q: Determine if the improper integral converges and, if so, evaluate it. dx | 8+x Write F if the…

A: The improper integral given is- ∫0∞dx8+x To find whether it converges or not . If integral tends to…

Q: V2x + sin? r Determine whether the improper integral da converges or diverges. Show all your steps.…

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Q: se the Comparison Theorem to determine whether the integral is convergent or divergent. 00 2 + e-X…

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Q: ex Figure out whether the improper integral dx is J_1 (1-e*)2 convergent or divergent. If it…

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Q: Find the indefinite integral. a. fsecy (tany - sec y )dy b. f(x²-9)(2x)dx

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Q: For what values of is the following integral convergent 1 to infinity 1 / xp  dx

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Q: -0.1x dx e 1 8.

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

Q: Q1) Evaluate the following integral: y = | tanx dx

A: We have to evaluate the integral:y=∫tan3xdxy=∫tan2xtanxdxy=∫sec2x-1tanxdx                Using…

Q: Determine if this improper integral will diverge or converge dx (x² – 1)4/3 1 Apply this in solving:…

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Q: 2 Given Rn 2 + cos ( 2 + i- , express the limit as n → ∞ as a definite integral, that is provide a,…

A: To find the following terms in the integratiin given definition of integration.

Q: 3 dx VI(x+1) 01

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Q: V2x + sin? æ Determine whether the improper integral dx converges or diverges cos? x

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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.