Use the integration by parts to evaluate the following integral by assuming u = COS 2 dx (cos a + a sin aæ)2

Q: Approximate the following integral using the Simpson's 1/3 rule. SO, (cos a) da 0.25 2 -0.25

A: Given,∫-0.250.25cos x2 dxfx=cos x2a=-0.25 , b=0.25 , n=4h=b-anh=0.25--0.254h=0.125

Q: Use the table of integrals at the back of the text to evaluate the integrals ∫sin t/3 sin t/6 dt

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Q: Consider the following integral: sinx dxdy By reversing the order of integration, the value ofI is…

A: In the question, the limit of x is a function of y. We will change this order and put y within a…

Q: Use the Table of Integrals to evaluate the integral. T4 - 9 sin e sin 20 de 4 – 9 sin 0 |

A: We use substitution to integrate the given function.

Q: Evaluate the integral. (Use C for the constant of integration. sin (0) cos“(8) de

A: Given: ∫sin3(θ)cos4(θ)dθ

Q: Use Romberg integration to compute R33 for the following integral x sin x dx

A: The solution is

Q: Evaluate the integral. (Use C for the constant of integration.) A) x cos(2x) dx B)e6θ sin(7θ) dθ

A: here we evaluate the integral      (A)   ∫ x cos (2x)dx     (B)  ∫ e6θ sin (70) dθ

Q: Use integration by parts to evaluate the following Integral S3 cos x? dx

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Q: b. I = S(1+ sin x)5 cos x dx

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Q: (x² + 2x) cos(2x) dx

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Q: I = S(1+ sin x)³ cos x dx

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Q: Evaluate the following integrals.

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Q: Use a substitution to change the integral into one found in the table of integrals, then evaluate:…

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Q: Evaluate the integrals using the indicated substitutions.

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

Q: sin(6x) Vi? +4 dt 7

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Q: Evaluate the integral by making a u-substitution and then integrating by parts. NOTE: Enter the…

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Q: Write the integral as a sum of integrals without absolute values and evaluate: Leis | cos x | dx =…

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Q: Evaluate the integral by making the given substitution. (U | cos12 0 sin 0 d0, u = cos 0

A: Given : ∫cos12θsinθdθ

Q: Find a bound for the error in the approximation M20 to the given integral (but do not calculate…

A: The given integral is ∫0π35cos(x)dx. To find the bound in error use the midpoint  rule which is…

Q: tan(x)dx, Ind: u = cos(z)

A: We have to calculate the given integral: ∫tan x dx We know the identity, tan x=sin xcos x Therefore,…

Q: To evaluate the integral /V4 + x² dx using a trigonometric substitution, use the (4+: substitution…

A: NOTE: Refresh your page if you can't see any equations. . .............(1) substitute…

Q: Evaluate the following integrals S, sin () cos" () dx ) dx

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Q: Evaluate the integral using the given substitution. Sx cos (10n2) dx, u = 10x² sin (10x²) - C sin…

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Q: If necessary, use two or more substitutionsto find the following integrals.

A: The given integration is I=∫0π2cosθsinθcos2θ+16 dθI=∫0π2cosθsinθcos2θ+16dθsubstitute…

Q: Integrate the following integrals using either integration by parts or integration by substitution.…

A: I=∫e-2θsin6θ dθ Integrating by parts, we get I=∫e-2θsin6θ dθ=e-2θ∫sin6θ dθ-∫de-2θdθ×∫sin6θ…

Q: Find the integral for the following : dx 2- fe-*sec? (ne-*)dx 3- Sdx ZVI+2x 1+e*

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Q: Evaluate the integral in the form a sin(u(x)) + C for an appropriate choice of u(x) and constant a:…

A: given,         A=∫x2cosx3+1dx

Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

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Q: Evaluate the integral using the given substitution. Jx cos (5x?) dx, u=5x? O A. sin (5x2) +c 1 O B.…

A: Note:Since you have asked multiple question, as per our guidelines we are supposed to answer only…

Q: Evaluate the given integrals. 4. J(secx + tanх)? dx

A: Given problem:- ∫ (tan(x) +sec(x))2 dx

Q: By using a trigonometric substitution x = 3sece ,where 0 s0 < 27 "he integral 3 Vx² - 9 dx can be…

A: We have to choose the correct answer from the given option according to the given condition

Q: Consider the following integral: sinx dxdy I By reversing the order of integration, the value ofI is…

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

A: Given: ∫19x2+4dx Let I= ∫19x2+4dx To solve this we need to the trigonometric substitution

Q: 7. Use the Method of Substitution for Integrals to evaluate the following integrals: A. x? cos x3 dx

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

Q: 3n/4 cot a In(sin r) dx

A: Use integration by parts

Q: Use integration by parts to find the integrals shares e) f sin? @ de f) esint sin2t dt 8) x²e-* dx…

A: Evaluation of the Integrals

Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

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Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

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Q: Which of the following integrals will represent the area outside r = 3, but inside r = 6 sin(0)?

A: area = 12∫ab[outer2 - inner2] dθ

Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

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Q: Use the table of integrals at the back of the text to evaluate the integrals ∫e2t cos 3t dt

A: Given, ∫e2tcos(3t)dt

Q: Consider the following integral: sinx dxdy By reversing the order of integration, the value ofI is…

A: In the question, the limit of x is a function of y. We will change this order and put y within a…

Q: Evaluate the integral by making the given substitution.   ∫ Cos3θ Sinθ dθ   ,  u= Cosθ

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Q: Consider the following integral: sinx dxdy I = 'y By reversing the order of integration, the value…

A: Value of I=∫0π∫yπ sin xx dxdy  by reversing the order of integration.

Q: [9 cos (12 – 6t +1) dt 4

A: Solved below

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

A: Given integral: Now,

Q: Is the integral formula correct? Sxsinx sin x dx = - xcos x+ sin x+C

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Q: Evaluate the integrals

A: We have to evaluate the definite integral: ∫-ππ1-cos2 t32dt We know the trigonometric identity, cos2…

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.