To solve J- -dx using a suitable trigonometric substitution, the integral can be rewritten as fkg(®)de. V4+9x² Which of the following is the resulting integral of Jkøle)de? Oa. 1 In(sece +tan@) + c Ob. 1 In(secêtane) + c Oc. 1 In(sece + tane) + C O d. 1 (sece + tane) + C

Q: To find the arclength of y = 2x2 – 1 from æ What is the value of the integral? O to x = 3,

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Q: Evaluate the integral using the trigonometric substitution x = 4 se dx 5. x² Vx2 – 16

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Q: Evaluate the integral. cos(z) dz sin? (z)

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Q: Given Tex+4 dx. Using a suitable trigonometric substitution, the resulting integral in terms of 0 is…

A: Given ∫19x2+4dx Let substitute x=23tanθ. dxdθ=23sec2θdx=23sec2θ Substituting the value, we get…

Q: 21. Given the integral [ cot³x csc ³x dx. If u = cscx, then the integral can be re - written as:

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Q: Given: 5x2 tan ( 3x) dx. If u=3x³, then the resulting integral is Jf(u) du. Find. 4

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Q: To evaluate the integral 23 V2-2x 3 da, using trigonometric substitution, which substitution should…

A: Given, ∫x3x2-2x-3dx Find which trigonometric substitution is used to evaluate the above given…

Q: y? dy = In Vy² + 3 + y V3 5. y :+C (y? + 3)i /y² +3

A: on solving this we get the

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A: We are given with the integral and evaluated

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Q: evaluate using trigonometric substitution. Refer to the table of trigonometric integrals as…

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Q: Consider b sin() dx where a, b E R. Which of the following selections result in the integral…

A: I=∫ab sin2x5π dxI=1π-cos2x525abI=52π-cos2b5+cos2a5I=52π2 sin2b+2a5(2)sin2b-2a5(2)I=5π sin(b+a5)…

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Q: Use the indicated substitution to evaluate the integral. -3 cos x sin (sin x) dx , u= sin x 3 sin…

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Q: V1 +x² – 1 In dx 8. xV1 +x? + C

A: Solving the given integral.

Q: S dy 2 2 +1

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Q: Use the calculus of residues to evaluate the following integral 27 1 de. 1+8 cos? 0

A: Given integral is ∫02π11+8cos2θdθ

Q: 't + Vt2 - 36 In dt J ले +C t2 -36 6

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Q: The resulting integral of sin-cos-sino de has the form -F(@) +C What should be the value of e to…

A: We know that integration of sinx is - cosx and we know that trigonometry relation is  Sin2x =  2sinx…

Q: 4x² – 25 7. = sec 0 dx

A: 7) a)Evaluate the integral using the indicated trigonometric substitution. b) Sketch and label the…

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A: As the question only demanded the trigonometric substitution so I have only solved just to reach the…

Q: 1. a° cos(2)da = %3D

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Q: state the trigon metri e subs tition you would use to Find the indefinite integral Do Not integrate.…

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Q: Evaluate the integral using Trigonometric Sub. 3 (e2z + 8e² – 9)¯ždz

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Q: What trigonometric substitution will you use in solving the below integral? Note: Let W be the…

A: We will evaluate this integral as shown below

Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. In 4…

A: We need to substitute e^t = x to solve it.

Q: Using trigonometric substitution, the integral -dx would result to M 9-x2 N?dt,what is M and N? (N…

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Q: The appropriate trigonometric substitution to evaluate the integral - z+3 dz is: Select one: O a.…

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Q: хах 2. S (V16-x2) 3

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Q: To solve dx using a suitable trigonometric substitution, the integral can be rewritten as Skole)de.…

A: To solve: ∫14+9x2dx Let I=∫14+9x2dx To solve this, we need to apply trigonometric substitution…

Q: Evaluate the integral (Trigonometric Substitution) 1 (n²z6 – z®)ždz

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Q: If we change the integral fS drical coordinate, then the result integral will be: x dzdydx to cylin-…

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Q: To evaluate x?V1– x²dx using trigonometric substitution, what is the new integral in terms of .a? 1…

A: Simplify the integrand using the formulas below .   sin2θ=2sinθcosθsin2θ=1+cos2θ2sin2θ+cos2θ=1

Q: Consider the integral given below. | (2 - 5z2) dz Which of the following answer choices is true?…

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Q: |a° cos (2") dz = +C. Hint: First make a substitution and then use integration by parts to evaluate…

A: Given query is to find the integration of the expression.

Q: x2 dx 3. (бх2—49)"/2 49 [V36x3-9x IVox + v6x2 –9 + In + C I 12v6 49 7

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

Q: The resulting integral of sin-cos-sino de 2 2 has the form -(0)+ C· What should be the value of o to…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Given the integral S5x+ cos(7s) dx Use the technique that we went over in class to find "u", "V",…

A: Given ∫5x*cos7xdx   using by parts technique determine u, v and du

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A: One of the two main parts of calculus which are concerned with the study of integrals, as opposed to…

Q: or each of the following integrals, indicate the trigonometric substitution that could be used to…

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Q: For the given integral dx sin2x/1+ cotx what is u? note: no space between symbols in your answer

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Q: Evaluate the integral f v96 + 16x² dx using trigonometric substitution.

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Q: In evaluating the inte gral, Substitution leads to a now integral S f(u) du xST+2x dx 1 Correct for…

A: Given∫012x21+2xdx

Q: Which integral represents the area of R? Choose 1 answer: 5π 49 A sin² (40) de - 4 5TT 49 B sin²…

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Q: Which is NOT included in evaluating the integral? (Use the Trigonometric Substitution method.) dx 4…

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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.