Jsing substitution with u = sin(2x), the definite integral sin3 (2x) cos(2x) dx is equivalent to u³ du 1 B u³ du 2

Q: 4. e2x sin e*d x, use algebraic substitution

A: Given :  Intergral ( e2x sinex dx)

Q: Integrate S(cos x)e*+sin xdx B. et-sinx + C A. -e4+sin x + C c. e4+sinx + C D. e-4+sinx +C A В C D

A: Given: I=∫cosxe4+sinxdx  ....(1)   We know that; ∫eax+bdx=1aeax+b+C

Q: 2:)y= 2x cos G) yous? (x²) +y sin² (x?) 2

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Q: Bonus: Evaluate the integral  ∫ cos2 x dx

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Q: cos(x)In(1 + x²) + æ4.8 dx. Evaluate 1+ el.69z – 42.8 answer =

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Q: dw Use the Chain Rule to find where w= cos 12x sin 4y, x=5, and y =t". dt dw dt (Type an expression…

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Q: using the substitution u = cos(x). cos (x) sin(x) dx = +C

A: We have to find the integral ∫cos5(x)sin(x)dx

Q: y = x sin-'x + v1-x² What is dyldx? " v1 - x2 x tan-1x >>>> >>> cos-'x sin-'x

A: The given function is: y=x sin-1x+1-x2

Q: S x dx x²+√√x²-1-1 The integral substitution? (A) [sec²0d0 1+tan cose de (B) 1-sine sece tane de…

A: Simplify and substitute x = sec θ to get the answer.

Q: Q2- i) Evaluate the following integrate 3 –dx 1+sinx

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Q: T sin(x) cos(x) dæ = Hint:

A: Topic:- integration

Q: Homogeneous Find C, if y f(cos 2n) = tan 45° 3(3x + y?)dx-2xydy 0

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Q: f (t) = e(-3t) sin(2t) cos(3t) cosh(t)

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Q: Bonus: Evaluate the integral (10 pts) cos'x dx

A: To solve this question we have to remeber one basic formula of triogonometry which is: Cos2 x = (Cos…

Q: 2 x+1 2) Evaluate f,“ dx using the substitution u 3 Зх — 2 V3x-2 3) Evaluate f2 e cosx dx

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Q: x dx x² + √√x². The integral - sine de SSH 1 + cose sece tane de sece - 1 sec²0 do 1+tano cose do…

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Q: f(x) = 2 sin(cos z)

A: Given,           y = 2 sin(cos x)

Q: Integrate the following using the substitution method. a) Te* cos e dx 2x+1 3x² +3x

A: We will use substitution method to evaluate these integrals.

Q: Find the indefinite integral. |x cos 9nx? dx х сos Step 1 To find the indefinite integral x…

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Q: Original Sound ff EXERCISE dy -x = x2 siny dy 3 -(-siny ANSWER: X = %3D

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Q: Q1: Answer A OR B A - Evaluate the following integral. e2x cos3x dx

A: let I=∫e2xcos(3x) dxlet  u= cos(3x) ,  v =e2x I= ∫cos(3x) e2x dx∫cos(3x) e2x dx=…

Q: (x*+ x) : 2 cos x -1+ 2 %3D dx (use rules)

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Q: xcosx dc + Cos x da 2.

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Q: Use substitution to evaluate the indefinite integral | cos³t sint dt. [Hide Solution] cosʻt + C 4

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Q: Evaluate cosh² x dx 0 (sinh2n +a). +x) + C O2e² +42 + C 8 O None of the choices O cosh(z)sinh(z)++C

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Q: Q: Classify and Solve dy sin x dx sin x sin 2x +y cos x

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Q: Q/ solve the differentil-equation ty-f'sinx-x)+(3xy+2y.cosx)

A: We will solve the problem.

Q: Z=sin(X) + cos(Y) X from 1 to 10 (increments of 0.5)

A: % Matlab script to create 2 subplots (mesh and surf) % create the matrices X, Y both between…

Q: The integrating factor that can be used to turn the following non-exact equation into an exact…

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Q: Q2- i) Evaluate the following integrate 3 dx 1+sinx

A: Since there are multiple question , we solve the first one . Post the other question again. ∫31+sin…

Q: The coefficient of sin(x) in the antiderivative of F(x) =| cos 2 %3D

A: Given: F(x)=cosx26

Q: the substitution formula to evaluate the integral. 4 cos³ x sin x dx T/3 27) 15 A) 15 B). 15 3276 D)…

A: Given query is to find the value of the integral.

Q: (z*sin - 2° cos 2y cos r2 y? dr+2xy cos ,dy = 0.

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Q: d²y Let y = sin (ax + b) ldentify the value of from the following: dx? -a² cos (ax + b) -a² sin (ax…

A: Given y=sin(ax+b)......(1)

Q: dx J x²–18x+97 O fIn (x² – 18x + 97) + C In (x² – 18x + 97) + C 0sin-l (부) + C х-9 O tan-' () + C…

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Q: dy There is no need to simplify. dx 2. Find cos- (sin x) – sech(tan-x) a. y = ecosh a

A: Find your answer below

Q: (ii) Evaluate J dx. COS TI

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Q: Can someone show me how to reach this answer shown in the problem?

A: Given,

Q: We would like to evaluate d sin(t?)2tdt dx Compute f (x) = S*, sin(t²)2tdt Find f' (x). (a) (b) (c)…

A: To solve the problem uaing fundamental theorem of calculus

Q: 2sinx (x)cos (x)dx = (a) (b)를 (9); (d) (e) Nor a

A: Since you have asked multiple questions in single request.so we will be answering only first…

Q: Let a > 1 be a constant and y = (10e¬ sin z 6) In(r+a) . Find y'(0). %3D

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Q: cos z Can you use p instead of p- 1+ z2 eiz to obtain the integral for cos x dx? o 1+x2 1 + z2

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Q: Using substitution with u = sin(2x), the definite integral sin (2x) cos(2x) dx is equivalent to ...…

A: Use substitution

Q: Using substitution with u = sin(2z), the definite integral si "sin®(2x) cos(2r) dr is equivalent:…

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Q: 2T d) f(x)=5 sin (x+1)+2 e) f(x) = -2 cos 2(x+ 1) + 1_ 17. Find the rule of the sinusoi

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Q: Q1) Show that: (a) (1+x)° =1+6x :(cosx) = dx = -sinx (e)읊 = E d ( V) = (d) V1+ tan x = 1+;x dx 2 vx

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

Q: sinx b) Find dx if m t2 + 5 dt + cscx + y = x cosx 10 b) Find for sin?x + cos?y = dt xtany t+2 dx

A: b) we know that  ddx∫f(x)g(x)H(t)dt=[H(g(x)g'(x))-H(f(x)f'(x))] we have ∫xsin(x)t2+1dt…

Q: C. Evaluate the definite integrals ( show your solutions) 1. S, (x³ – 6x² + 2x)dx - TT 2. 3 cos3…

A: The given questions can be done as follow:

Q: X Evaluate the integral [sincos dx. X sin cosdx= 5 C

A: The objective of the question is evaluate the indefinite integral.

Q: x² (d) √ √ 1 - 4.² (HINT: sin² t = ½(1 – cos 2t).) dx. Evaluate

A: Integration Using Trigonometric Substitution We use trigonometric substitution in this problem to…