Show that n/2 sin x dx sin x + coS X %3D 4

Q: 1. Integrate: [x³ sin(2x) dx.

A: As per Bartleby guideline, only the first question has been answered. If you want to get the answer…

Q: 6. S sin x In(1 + sin x) dx

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Q: Find the exact value. In 3 0 ³ sech 4 x tanh x dx

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Q: 1. -5 cosh x 2+3sinh x dx

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Differentiate. y = In Sin x  - 1/2Sin2 x

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Q: Solve the integral. sin x dx 10. cos2 x + cos x – 2

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Q: Evaluate the integrals

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Q: 1. [ (6x² – 2x+3)dx sin(2x)dx 3 2. 3. S2 8 dx X+2

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Q: 2 sin x dx cos x 7.

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Q: 4x sin(4x + 5) dx 3.

A: Answer is here

Q: 4. X sin (x) dx VI-X 1-メ-

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

Q: 5. . sin 3x dx

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Q: Find for y = 5x sin x+ 10x cos x- 10 sin x. dx Dikdörtg

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Q: .Find a reduction formula for ea* sin" x dx. Hence evaluate e* sin x dx. 3

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Q: aluate 9/ sin(x) cos(x) dx by four methods.

A: Here we want to perform the given integral according to each of the methods mentioned.

Q: 1 |sin xdx ーπ 3 sin xdx 5 S sin xdx

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Q: Find ∫e^(2x)sin(2x)dx

A: Given: ∫e2xsin(2x)dx

Q: Solve the integral. sin x dx 10. cos2 x + cOs x – 2

A: Given: ∫sinxcos2x+cosx-2 Let u=cosx, thendudx=-sinx and dx=-1sinxdu.…

Q: = (a) Evaluate S cosx sinx V1 – sin4x dx. -

A: Given∫cosxsinx1-sin4xdx

Q: 9. S sin(4x – 2) dx

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Q: Cos 2x dx ) Sin*2× + 8 1.

A: Given ∫cos2xsin22x+8dx

Q: S sin(4x + 3)cos(3x – 5)dx -

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Q: 3. S sin x sec®x dx

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Q: find integral sin 5 x  cos 2  x dx

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Q: 9. sin“ x cos“ x dx

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Q: find dy/dx 4x -x 2x 23) y= Sin- +x².Sec 2-x + 2x.Sec) 2 (ans.: (2-2»N(2-x² - x* 4 4

A: To find the dy/dx means y' of the given function

Q: 비신부 4 x² sin(2x) dx

A: Given : ∫827dxx-x3

Q: 2. Integrate | sin x cos? x dx

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Q: Show that sin(x^2) ≤ sin x for 0 ≤ x ≤ 1. Deduce that sin(x^2) dx ≤√2/2 on the invterval [0, π/4]

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Q: 3 sin x 1. S- dx 1+cosx

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Q: 1) | xe3*dx хе 2) | x2 sin x dx 3) x sin 2x dx

A: Since you have posted a question with multiple sub-parts, according to company guidelines we will…

Q: S sin (3x) 1+cos² (3x) dx

A: Given integral ∫sin(3x)1+cos2(3x)dx The objective is to evaluate the integral.

Q: Find cos x + sin 2x dx 19. sin x

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Q: 8. Find if y (sin x + cos x) sec x dx

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Q: 2 sin x cos8x dx

A: Given- ∫0π2sin6xcos8xdx To Find- The value of the above integral. Identity Used- The value of the…

Q: 16. S sin 3x cos 3x(cos 3x+1)² dx

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Q: 4). | (5 sin 2x) dx = 2

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Q: 4. S sin¯ 3x dx

A: We can solve the given problem using integration by parts . According to Bartleby guidelines I have…

Q: Evaluate 不12 Sin^ x dx = 「ズ「() 2 2r/2+2 n > -1 (Gamma function).

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Q: 5. S sin5x cos 3x dx

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Q: S sin x (1+ cos 2x)² dx

A: In some cases integrals can be converted to standard integrals using an appropriate substitution.…

Q: Find the extreme value/s of f(x) = 4 sin² x − cos 2x on . (³347) 3π 5π 2' 2

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Q: S sin(3x + 5) sin (4x – 7)dx

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Q: dx |2 sin 2 sin x — сoS X

A: I have appended the formula used in the solution part

Q: 6. sin x cos°x dx

A: We need to evaluate integral.

Q: Evaluate the integral.

A: Given: I=∫0π4xsinxcos3xdx

Q: •/2 sin x cos x dx

A: To find:

Q: S sin(3x)cos(2x)dx

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Q: a. dx 1+ sin(ax)

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