sin?x dx Vx3

Q: Evaluate the definite integral (1+lnx)? dx a.

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Q: Evaluate each integral bY first making an a substitution. appropriate Sx(x²-1)" dx ल मैंढ a)

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Q: Determine whether each of the following integrals is proper, improper and convergent, or improper…

A: As per Bartleby's answering policy, we can answer only one question with a maximum of three…

Q: Find the indefinite integral.

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Q: State whether the following integral is Convergent or Divergent. e*dx 8. O Convergent O Divergent

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Q: dx sin 3x cos 4x

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Q: Determine if the following integrals converge or diverge by using the indicated tests next to them.…

A: According to the given information it is required to determine whether the integrals in each part…

Q: e dx e2x+1

A: To evaluate:∫exe2x+1dx

Q: aluate the following definite integral by using the properties of Beta and mma functions. sin'x dx o…

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Q: [(x-1)sin zxdx

A: Given:  Let I=∫x-1sinπx dx To Find: To evaluate the given integral.

Q: x 45. 0 xª – 1

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Q: Determine whether the following integral converges or diverges. a) 6.00 ㅠ b) fo X (x² + 1)² tan x…

A: Let us determine whether the integral converges or diverges in the next steps.

Q: use a geometry formula to find the exact value of the definite integral  lxl dx on the interval…

A: Line AOC represents the graph of y=mod x in interval [-2,1]. Here coordinates of 0 are (0,0), A are…

Q: Does the following integral converge or diverge? Justify your answer. 112 dx Vx*+13

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Q: Evaluate the integral. (Use C for the constant of integration.) dx /x² + + 81

A: In this question given that a integration and solve it.  We use here integration formula and solve…

Q: Evaluate the integral. (Use C for the constant of integration.) dx x² + 81

A: Use substitution method to integrate. or   use ∫secθ dθ = logsecθ + tanθ + C1…

Q: sin (x), dx b) J∞ 4+x²

A: Given improper integral: ∫-∞∞sinx4+x2dx Let x2=4tan2θ         x=2tanθdx=2sec2θdθ Substituting these…

Q: Determine if the following improper integrals converge or diverge dx 2) 1 + e-2x -8

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Q: Q2) Find the integral of: 6 tan*x dx

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Q: 4. Use the comparison property to calculate if the following integral converge: sin? a dx. V1+x3

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Q: 4. Use the comparison property to calculate if the following integral converge: sin? x dx. | 1+

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Q: Evaluate the following definite integral. If the integral diverges, say so and why.

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Q: Evaluate the integral I sin(x)e-" dx.

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Q: cos(x* + 2) dx

A: To Evaluate: ∫x3cosx4+2dx Concept: ∫cosxdx=sinx+C

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

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Q: a) S In Gxt1) dx 2.

A: In this question we have to find the Integration. Formula Used, - Chain Rule. - ∫lnx=1x+C

Q: Evaluate the integral. x sin(2x) dx = +C

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Q: Which of the following integrals is convergent? Select the correct answers. .24 0 of OP 0 2 X dx dx…

A: We have to find which of the following integral is convergent. (a).…

Q: 3. Find each of the following integrals using any suitable techniques: (d) sec® 4x tan² 4r dx

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Q: Which of the following integrals converge? If they converge, evaluate them. (a) | x log(a) dx, (b)…

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Q: ) Does the following integral converge or diverge? Prove your sin? (x) dx x3

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Q: 1 dx 1+Vx

A: Explanation of the answer is as follows

Q: 5 -dx x² –4

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Q: Use the appropriate technique of integration to solve the following. (a) In x? + 1dx

A: SOLUTION-

Q: Evaluate the integral tanh (2x)sec h? (2x) dx.

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Q: n4 dx b. 2 х-3

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Q: Does the following integral converge or diverge? Justify your answer. 112 dx /x°+13 8

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Q: find formulas for the functions represented by the integrals.

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Q: Consider the integral (ln(x))6 dx:

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Q: 2 sin²(x) cos(x)dx

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Q: -1 4x° sec x dx

A: In this question we will use basic concepts of calculus i.e concepts of indefinite integration. We…

Q: Find the integral of the following function: sec? (x) dx 1+ tan(x)

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Q: Use the Comparison Theorem to determine whether the following integral is convergent or divergent. 4…

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Q: Evaluate the integral - dx · 1- sin x cos X

A: The given integral,       ∫cos x1-sinxdx

Q: Evaluate this integral I = ∫ a 0 x^2 √(a^2 - x^2)   dx. Then determine whether the statement is true…

A: Given integral is,

Q: use a geometry formula to find the exact value of the definite integral (-2x+4) dx on the interval…

A: We have to find the exact value of the definite integral (-2x+4) dx on the interval [3/2,1/2]As a…

Q: For what values of  a is ∫0∞ eax cos x dx convergent? Evaluatethe integral for those values of a?

A: ∫0∞eaxcosx dx Now, ∫0∞eaxcosx dx=limt→∞∫0teaxcosx dx=limt→∞eaxa2+1acosx+sinx0t    ∵∫eaxcosbx…

Q: Determine whether the integrals below converge or not. Do not try to evaluate them. (a) dx 1 d.x 1…

A: As per the question, we need to determine whether the given integrals converge or not without…

Q: Find the following improper integrals and then state whether it converges or diverges. a) S," In…

A: The  improper integral is given as ∫1∞lnx2dx To find : whether the given  integral converges or…

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.