4. (cos? 6x + sin 6x – sin³ 6x)Zdx (Hint:factor out sin 6x first) 3 -

Q: Q4:B/Simplify [cos 20-i sin2018[cos 30+ i sin301² [cos 40+ i sin40]³[cos 20-i sin2015 using De…

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Q: Evaluate [(1 +x-3 + sin4x)dx -2 cos4x X - + c 4 0x-- cos4x + C cos4x O 2x- 4 0 4x-두-5t +c cos5x + c…

A: As we know that the integration of : ∫fx±gxdx=∫fxdx±∫gxdx ∫xndx=xn+1n+1+c ∫sinxdx=-cosx+c

Q: 1 Show that L-1{ = (sin hat sin at) s4+4a4, 2a²

A: It is given that, L-1ss4+4a4=12a2sinhat sinat. A partial fraction decomposition of ss4+4a4:…

Q: If +a= a(2 cos 0 cos 20) and y=a(2 sin0 sin 20),show that (z² + y² + 2az) = 4a² (z² + y²). %3D

A: Given that, x+a=a2cosθ-cos2θ⋯⋯1y=a2sinθ-sin2θ⋯⋯2 Squaring both sides of (1) and (2) and adding,…

Q: 4sin 5x cos 3x-4cos 5x sin 3x/rom x= 0 to x= 2m

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Q: 11. Evaluate the integral: tan 2x dx A. -In| sec 21| + C -sec² 2x + C С. -In| cos 24| + C D. 2 sec…

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Q: Show that (1-)dy+(cos xsin x-sy")dr =0 is an exact equation. Hence, find its general solution. Hint:…

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Q: 5. S(sin3x + cos2x)²dx

A: To find : ∫sin3x+cos2x2dx

Q: 1 In [cos"-1 (3x) sin (3x) +3(n – 1)I-2] 3n 1 h= sin (3r) %3D What is I, ? I.

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Q: The suitable substitution to evaluate / sin²4(x +2) dx is (1- cos8(r + 2)] [1+cos8(x+2)] None 1 [1-…

A: We have to find the suitable substitution to evaluate the following integral -  ∫sin24(x+2) dx

Q: Show that L-1{ = (sin hat sin at) s4+4a4, 2а2

A: To find Inverse Laplace transform of ss4+4a4: write ss4+4a4 as  ss2+2a22-2as2 Then the denominator…

Q: 4 sin (3z) dr

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: sin (2t + 1) - dt cos? (2t + 1) 31.

A: Use trigonometric substitution method for solving the integral.

Q: The integral ¹S. 01-fese csc ³0 de sin² sin ²0 de = [sec³ sec ³0 de + cos² cos²0 de dx (x²+4)² can…

A: We have to solve Integral

Q: 3. If y = (sin 4x)², find y' %3D a.) 4 sin4x cos 4x b.) -4 sin4x cos 4x c.) -8 sin 4x cos 4x d.) 8…

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

Q: 4. Evaluate 5 cos x dx 3 v2 sin x – 1

A: To evaluate : ∫π6π3 5 cos x32 sin x - 1 dx

Q: b) sin 3x 3 sin x – 4sin3 x [Hint: sin 3x sin(2x + x)] Prove

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Q: Q4:B/Simplify [cos 20-i sin2018 [cos 30+ i sin30 1² [cos 40+ i sin40 ]³[cos 20-i sin2015 using De…

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Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x %3D

A: NOTE:according to company rules I need to solve first question when multiple questions are posted

Q: 3 (4+sin-15x)° dx (8) V1-25x2

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Q: 2 sin 2x - 1 de hift -2AT Chift

A: The standard form of the trigonometric function ,y=asinbx-c+d. The given function is y=2sin2x-1.…

Q: 2 3. sin³x cos³x dx OSx Show two solutions. 0.

A: Given  The integration is I=∫0π2sin3x cos3x  dx.

Q: 5. Find y', if y 2cosx sin2x – sinx cos2x %3D

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Q: (3.2 cos 2x+2 -dx. 1.8 1+ In x Use NINT on the calculator to evaluate:

A: We have to evaluate ∫1.83.2 cos 2x + 21 + ln x dx.

Q: 3 .3 S sin 2xcos 2xdx

A: The objective is to solve the integration ∫sin32xcos32xdx Let, 2x=t⇒dx=12dt, then…

Q: To evaluate sin*2x cos 2x dx , the identities to be used is/are: 1+ cos4x A sin4x & 2 2 B cos²2x= 1-…

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Q: 1. y = In (3 – 4 cos x) + (4x – 5)5 2. y = x² tan x 3. y = x5 sin2x cos 4x %3D

A: We will answer the first three questions as per our guideline. Please resubmit the other question…

Q: 3. sin 3z cos 5z dr

A: Here we have to evaluate I=∫sin3xcos5xdx

Q: S cos(3r)(sin(3x) +5)10 dz Select one: (sin(3z)+5)" 11 +C O (sin(3r) + 5)"+C (sin(37)+5)" 33 +C…

A: Consider the integral: I=∫cos3xsin3x+510dx……1

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin301² [cos 40+ i sin40 1³[cos 20-i sin2015 using De…

A: The given expression,      cos 2θ-isin 2θ8cos 3θ+isin 3θ2cos 4θ+isin 4θ3cos 2θ-isin 2θ5 De Moivre's…

Q: Verify y = 4 cos(2x) + 6 sin(2x) is a solution to y" = -4y.

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Q: y cos?£ 1-CUSE tanzz

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Q: d. Show that sin 8x + sin 4x cos8x-cos4x = -cot(2x)

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Q: 8 and x terminates in guadrant IV. 15 Find sin 2x, cos 2x, and tan 2x if tanx %3D

A: Given  tanx=-815,  x in quadrant IV

Q: (i) Prove that sec 3x(sin 3x-2sin' 3x)= tan 3xcos 6x. (ii) Hence find, for 0s.xs, the values of x in…

A: Trigonometric equation

Q: 9-10.j Show that sin20 2tane %3D 1+tan20

A: We will prove the trigonometric formula.

Q: .15 S sin²4y cos>4ydy

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Q: (7) Find sin(5x) cos(4x) dx

A: Topic:- application of integration     Note:- as per our guideline if more than one question…

Q: 13T (b) sin-(sin(- -)) = %3D 11

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Q: 4 sin' 2x cos 4x dx 4.

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Q: Given: z = sin 3x cos 4y Find: z ду2 -3 cos 3x sin 4y -9 sin 3x cos 4y -12 cos 3x sin 4y -16 sin 3x…

A: Differentiate the given function partially w.r.t y keeping x as constant   ∂z∂y=sin 3x×4-sin 4y…

Q: = 2. If y = sin³ (-) cos³ (1) prove that y' = sin² (x) cos(x)

A: Topic = Derivative

Q: 3 Q19- if z =- 4x³y sin sin (x³y) əz find əx

A: We want to find partial derivative of the given function.

Q: The suitable substitution to evaluate | sin² 4(x + 2) dx is None O A. - cos8(r +2)] [1- cos4(r+ 2)]…

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Q: The simplified form of cos G- 13x) + sin + 13x V2 cos 13z + 2 sin 13æ O v3 cos 13z + sin 13x O cos…

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Q: Find sin 2x, cos 2x, and tan 2x if sinx= and x terminates in guadrant IV. sin 2x %3D cos 2x %3D tan…

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Q: (7) (4+sin-15x)° dx V1-25x2 3. dx (8) J Ja +x Vx

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Q: . Evaluate S sin' 2x cos 2x dx

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Q: b) Is S cos4xV2 – sin4x dx (2 – sin4x)³ + C true or false? show me

A: this is false because

Q: Suppose that 3π/2≤θ≤2π,  csc(θ)=11/4, find sin(θ)=______. (round to 3 decimal places)

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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.