Evaluate the integral using the given substitution. Jx cos (6x?) dx, u=6x? x2 O A. sin (6x?) +C 2 1 B. 5 sin (6x2) +c O B. OC. Oc. - sin (u) +C

Q: Evaluate the following integrals. Show the solution. 1. S csc? (7x + 5) dx 2. fx? sec (4x³ + 9) dx…

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Q: Evaluate the given integral using the substitution (or method) indicated. (x+ 9)e*+ 9) dc; u = (x+…

A: Given inlegral ,                       (x+9)2 I = ∫ (x+9) e            dx

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. COS s*(7t)…

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Q: Consider the following integrals 4 sin? x -dx x2 + 6 00 e9t dt i. e9t – 1" Mark the correct one for…

A: Step:-1 Since, we know cos2x = 1- 2 sin2x⇒2 sin2x = 1 - cos2x An integral is called convergent if…

Q: Evaluate the following integrals i. SxIn(x+1)dx sin (Inx)cos (Inx), 2 ii.

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Q: dy 1 Let u = tan-y sin y – cos y -

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Q: x2 + 2 dx x° + x •T/2 5. 3 6. t cos (t) dt

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Q: Evaluate the following integral using trigonometric substitution. 36x² - 49 7 S² dx, x> 3 x³ 2 √36x²…

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Q: Evaluate the integral sin? t cos t dt by making the substitution u = sin t. After substituting we…

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Q: Evaluate the following integral using trigonometric substitution. 7/2 1 0 dx 2 (4x²+1) ² What…

A: I have stated the used formulas in the solution

Q: Which of the following integrals are improper? Why?  integral 0 to 1  tan x dx

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Q: 2) Use the appropriate trigonometric substitution to transform the integral into an integral in the…

A: “Since you have asked multiple question, we will solve one question for you. If you want any…

Q: Approximate the following integrals using the Trapezoidal rule. c0.25 (cos x)? dx b. x In(x+ 1) dx…

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Q: a) Evaluate the following integrals by Parts 6) (lnx)² dx In x [√x 8) | Ir 8) In(x² + 4)dx 9) […

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

Q: Evaluate the following integral using trigonometric substitution. dx (1+256x?) dx (1+256x2) (Type an…

A: To find: The value of integral ∫dx1+256x232. Formula used: Trigonometric relation: 1+tan2t=sec2t.…

Q: Q2: Evaluate, numerically, the following integrals: T/2 sinx -dx by using Simpson's rule ( take n =…

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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: Consider the indefinite integral 5x+6 dx: a) This can be transformed into a basic integral by…

A: Given ∫e5x+6 dxLet u=5x+6 →dudx=5→dx=15du

Q: #2

A: To find out the integration.

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

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Q: Evaluate the following integrals : a - Sesecx. sin x dx cos? x b- S sin( In x) dx

A: a) ∫esecx.sinxcos2xdxb) ∫sin(ln x) dx

Q: Which of the following is one of the correct/convenient steps to evaluate cot-+dx _which will yield…

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Q: Evaluate the following integrals. (a) / (csc0)(1+ sin² 0 + sin 0 cot² 0) d0 (b) /: (e) / dr VI-2r2 +…

A: Part(a) We need to evaluate ∫csc θ1+sin2θ+sinθ cot2θdθ Consider: ∫csc θ1+sin2θ+sinθ cot2θdθ=∫csc…

Q: 2. Evaluate the following integrals using a suitable trigonometric substitution. (a) / a9- 2 da (b)…

A: Solve both of integral in the following way:-

Q: L? + 1)? dx evaluate the Cauchy principal value of the given improper integral. x? (x² + dx 1)?

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Q: csch(3 tan x) + sin² x cos? x 1. d.x

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Q: Which of the following integrals are improper? Why?  integral -1 to 1    ( 1/ x 2 -x -2 ) dx

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Q: Using an appropriate substitution, the integral f e cos(e* + 1) dx is equal to:

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Q: Evaluate the following integrals i. L Ix| e(1+x*) dx -0.5 ii. So x cosh(x² + 1) dx

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Q: By making an appropriate substitution, which of the following integrals is equal to dx J* (x² – 9)52…

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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: Which of the following is an improper integral? - dx x² – x – 2 In3e cOsx Ax xe 'dr -2 dx 2x + 8…

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Q: Which of the following integrals is equal to the integral / f(3x – 5) dx? 713 f(2) dz 7/3 f(2) dz -2…

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Q: Which of the following integrals are improper? Why?  integral 0 to infinity    e -x 3 dx

A: integral 0 to infinity e -x 3 dx is an improper integral. Since the upper limit of the integral…

Q: 4cosx dx u = 1+ sin' ?x du %D

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Q: Evaluate the following integrals: 1. S (cos x – sin x) dx 2. ſ cot²x dx 3. S (sin x + x) dx

A: As per Bartleby answering guidelines if a questions has multiple subparts then an expert is expected…

Q: ch of the following integrals is equal to the integral / f(3x-5) dx? ) dr? 7/3 ) dz

A: Please refer to the image below

Q: Given the integral 5x dx x2 - 1 Use the technique that we went over in class to find "u", "u' ", and…

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Q: Evaluate the integral below so that the resulting antiderivative involves two terms and C. sin° x…

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Q: Which of the following is an improper integral? -4 x² – x – 2 In3e COSX dx xe -2 In(x++ 1) dx -1 dx…

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Q: Show that the integral ((? -1) (x+ 1) dx can be evaluated with any of the following substitutions.…

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Q: Which of the following integrals is equal to the integral /f(3x – 5) dx? -2 7/3 / (:) dz -2 7/3 5.…

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Q: Which of the following is one of the correctIconvenient steps to evaluate| cot-4dx_which will yield…

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Q: Secos(sin-tw)dv dv S- e2cos(sin¬{w) – 4 dv S- 4+ ecos(sin-w)

A: To find the values of dv such that the antiderivatives(integrals) exists.

Q: 5. Evaluate the following integrals using geometry. a) (1-2) (1 – x) dx 10 b) - 5| de 25 x2) da

A: A detailed solution is given below. Area of triangle = (1/2) (base) (height) Area of semicircle =…

Q: Which of the following integrals is equal to the integral / f(3x – 5) dx? 7/3 zP (?)f s(2) dz 2. 7/3…

A: Topic = Integration

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

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Q: Evaluate the integral. T/6 | 9 sec'x dx 2. п/6 |9 sec?x dx = 3/3 (Type an exact answer.)

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Q: Which of the following integrals are improper? O " tan xdx dx -dx L2+1 .2 dx -2 x+1 Se*dx None of…

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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.