Evaluate the integral using the given substitution. 5- sin cos dt, u= 5- sin- cos 1 O A. 5- sin 3 t sin, +C 3 O B. 2 5- sin +C c. 2 5- sin +C OD. 5 - cos + C

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: 1. cos50 sin³0 de TL 2

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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: Consider the following integral a2 /9 + x² After making the trigonometric substitution x = 3 tan 0,…

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Q: a) Evaluate the integrals using appropriate substitutions. dx Sino i)S i) f de Cos? 8+1 1+16x2

A: as per our guidelines I am solving only first question with both parts a(i) ∫dx1+16x2ii ∫sinθcos2θdθ

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: Of the following improper integrals, which exists and is finite? Select one: 1 sin – dx. а. 1 1 dx.…

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Q: Evaluate the following integrals (a) S Cos(2nWt)dt, where W is a constant. n/2 c3 (b) S,"7² S, r²…

A: Integral of cosx is sinx  Integral of sinx is -cosx.

Q: b. fsin (x)cos (x) dx

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Q: Evaluate the integral T 22 P" sin cos e de dode Hd 0 H₂

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Q: Evaluate the improper integral or state that it is divergent. 36 dx (1 + x2) tan - 'x O A. 36 In 1+…

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Q: Which of the following integrals represents the area inside the curve r = 3 + 2 cos 0 and outside…

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Q: By making an appropriate substitution, which of the following integrals is equal to | tan (x)…

A: make a substitution for choosing the integral.

Q: Evaluate the integral: - S- de. 4- sin?e cose A None of the given choices ® sin-(ino) +c B Sin-1 ©…

A: The objective is to evaluate the integral.

Q: Which one is a suitable substitution for the following integral? S -x²+4 x ○ x = 2 sec(t) O x = 4…

A: According to question,Given Integral,Let I = ∫-x2 + 4x dx

Q: By making an appropriate substitution, which of the following integrals is equal to de (D) e de (E)…

A: Let I=∫dxx3(x2-9)52

Q: I. Evaluate the following integrals. · cos³@de 4. S 1-sin® 5. S tan ( – x) dx

A: To Determine :-  The integral  4. ∫cos3 θ dθ1 - sin θ 5. ∫ tan  x4 - x  dx

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: TU f2 sin² p cos6 p dp

A: Solution is given below:

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

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Q: Consider the following integral: dx I = Vx - x² a. Use the substitution u = x - ; to show that I =…

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Q: 2. Given the integral: e/x dx;n = 8 d) Use the Trapezoidal rule to approximate the integral using…

A: When n = 8, then h = 0.25 and given f(x) = e1/x

Q: 2 | (8 + 4 cos 2) dæ

A: In this problem first we divide the interval into equal subintervals and the width of the…

Q: 3. Which of the following integrals requires integration by parts? A. S csc°0 de B. S cot*0 csc*0 do…

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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 integrals are improper? (Select all that apply.) dr 6x – 1 dr 2r – 1 sin (x)…

A: An improper integral is an integral that has either or both limits infinite or the integrand reaches…

Q: Consider the integral integral ^a b arctan(x)dx where-pi/4 is less than or equal to a which is less…

A: Let , The integral is I=∫baarctanxdx⇒I=∫batan-1xdx where , -π4≤a≤b≤π4

Q: Evaluate the following integrals using proper substitution: S sin? x cos3 x dx Hint: rewrite the…

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Q: Which of the following integrals are improper? (Select all that apply.) 1 dr 3r – 1 1 dr 2.r – 1 sin…

A: To decide which of the given integrals are improper.

Q: Evaluate the iterated integral. (T/3 cos(0) 3r? sin(0) dr d0 Jo

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Q: Evaluate the integral using the given substitution. x co 2 (3x) dx, u= 3x X COS sin (u) + C O B. sin…

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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 statements about integrals is true? | csc(x). cot(x) + C A) dx | sec(x) dæ =…

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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: ㅠ 10. fž sint p cos3 p dp 2

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Q: 3. Calculate the integral dz, (ke R), and use it to calculate the value of the integral cos(k…

A: GIVEN :-  The integral ∫z = 1 ekzz dz    k ∈ ℝ.

Q: TU 2. fz sin² x cos4 x dx J

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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: Which of the following is an improper integral? dx A 2x+8 cos (x)dx B -2 C -4x2-x-2 In(1+x*) dx -1

A: Improper integral is the integral in which function approaches to Infinity within in the given…

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: 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: Calculate the following Integrals: sin(3x) sin(a x)dx, a e R ahd j sin (3x)· e*a*dx, aeR, i the…

A: The objective is to calculate, ∫0∞sin3xsinaxdx It is known from trigonometry that,…

Q: Evaluate the double integral below. -27 S sr sin@drde 0. 0. O 5T О бл

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Q: What is the integral of f sin? x cos² x dx? O None of the choices O cos(2) sin* (z) cos(z) sin(z)…

A: Topic - integration

Q: Use the Composite Trapezoidal rule with the indicated values ofn to approximate the following…

A: As per bartleby guidelines we only give first question answers.

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: Evaluate the integral using the given substitution. sin- dx Select one: A.-1 +1 sin2 + C x 2 3 B.-1…

A: Given information:-

Q: The given integral is Te-x³(-3x²)dx. Let -x. Now differentiate u with respect to x. That gives U =…

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