3 y = Vlog2(sin5 x)

Q: Differentiate (a) y − sin(x2) and (b) y − sin2x.

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Q: 2 Evaluate sin2x dx

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

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Q: Integrate the square root of (1 - sin² x) dx.

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Q: 4si 2xcos²x dx sin2xcos2x

A: It is given that,     ∫4 sin2xcos2xsin2xcos2x dx We have to evaluate it.

Q: S cos³ x sinxdx

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Q: 2x sin- (x2) dæ dar 0,

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Q: Evaluate: #1) Sx² sin(4x)dx = %23

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Q: り plot s XE[-2T,27] Sin3X „Cas2X,

A: a.  Given function is, f(x)=e-x2 We find that f(0)=1 and when x→±∞, f(x)→0 So, the graph will be,

Q: sin S S. cossx (3-2secs)

A: The given integral is ∫sin 5xcos2(5x)3-2sec(5x)dx The derivative formula is ddx(sec ax)=atan…

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: Differentiate y=(1-cosx)/sin2x

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Q: Evaluate (a) 2. Sinx+ X=X (1) Sinx dx T+x²

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Q: 347. y = (sin 2x) 4x

A: We have to find the derivative of question 347 by using logarithmic function

Q: Integrate Sin (1-2 In v)

A: The detailed solution is given below Thank you

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

A: Given∫cosxsinx1-sin4xdx

Q: Use Substitution method: y' tan x sin2y= sin^2 x+cos^2 y

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Q: Find ∫sin3 x cos4 x dx.

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Q: 3. Find S sin5 x cos* x dx.

A: Use substitution method

Q: Differentiate y=(sinx)2(sin-1x)2

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Q: 3. f sin√tdt

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Q: Evaluate D(sinx – 4e2) (A -cos x-32 ex

A: The given function is sinx-4e2x. Evaluate the first derivative as follows. Thus, the first…

Q: Evaluate ∫ 3x2 sin(x3) dx.

A: To evaluate the integral  ∫3x2 sinx3 dx

Q: 2. Use the Intermediate Value Theorem to show that the equation sinx = x – 1 has at least one real…

A: In the question it is asked to calculate real solution of equation sinx = x-1. Also, it is asked to…

Q: 7. x sin(x²) dx = Choose...

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Q: 2. S sin 2xcos5xdx

A: To evaluate:∫sin2xcos5xdx

Q: Find Dg sin° (7x). 3

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Q: ) Evaluate cosx sinx V1 – sin4x dx.

A: Use substitution method to solve this

Q: Evaluate: cot[ sin! V212] O 2. O VZ 12

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Q: y= sin2x,

A: Given equation is: y=sin2x Differentiating with respect to x we get, dydx=ddxsin2x⇒dydx=2cos2x

Q: 1. ſ tan5 2x sec3 2x dx

A: Let,I=∫tan52xsec32xdxI=∫sin52xcos52x1cos32xdxI=∫sin52xcos82xdxI=∫sin42xcos82xsin(2x)dxusing…

Q: 3 y = Vlog2(sin5 x)

A: Given equation is y=log2sin5x3

Q: What is the antiderivative of  2(sin(2x))/sin(x)?

A: The anti-derivative of a function is a differentiable function whose derivative is equal to the…

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

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Q: sin4x S V cos4x + 1 dx

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Q: 2) Evaluate: |x sin5x dx

A: The integration of xsin5x.

Q: Differentiate: y = 8 sin(16x*)

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Q: Find Dx (sin4 x).

A: we have to find the value of Dxsin4x

Q: 3 y = Vlog2 (sin5 x)

A: The rational function dydx represents the derivative of the function. Differentiation of the…

Q: Number 17

A: First we break sin^3 x in sin^2x*sin x, and then we replace sin^2 x by 1-cos^2 x.THen in the next…

Q: Write the expression as an algebraic expression in x for x > 0.

A: Given: secsin−1xx2+4

Q: Find 6x2 sin x3 dx

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Q: 3 y = sin³ 2x

A: We have to use chain rule here.

Q: 3. Use trigonometric substitution to evaluate Sx V9 – x² dx

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Q: 2. Differentiate y = /sin(x² + 3)cosx

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Q: 2 2- Find if y = dx sin2x sinx

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Q: Determine 2 x sin x dx

A: We can find the integration as multiplication of two functions and then using ILATE rule to…

Q: Differentiate sin(x2 + ex) with respect to x.

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Q: Use the Substitution Rule to prove that∫sin2ax dx =(x/2) -(sin(2ax)/4a )+ C

A: Given:∫ sin2 ax dx