" sin(In x) tan dx 1+x? x sin dx V1-r

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

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Q: i sin(x) Evaluate the definite integral dx. cos(x)

A: We solve the given integral using the method of substitution. Also we know that, ddxcosx=-sinx.

Q: (a) f(x) = sin(x) X at x = 0.

A: a.the function is not defined at x=0. The function has right hand and left-hand limits same and…

Q: Find th epwation of the tangent line to An- (x-2y): 2xy-1 at print (1, 2) d [sin- (x-2g)] = (2xy-1)…

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Q: d Prove that (sin-l x) : dx V1 – x²

A: To show that:ddx(sin-1x)=11-x2

Q: Find dy/dx if y= tan-1(x/(1-x))

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Q: Q2 : Evaluate the integral sin x dx 1-sin² x

A: To find the integrations.

Q: Evaluate the definite integral. sin x dx -dx J12 I+cos² x

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Q: aluate the integral. Зл/2 3|sin(x)| dx

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Q: d Prove that 1 da (sin-1æ) = V1 – a? -

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Q: SHE 1+ (In x)' = dx = (sec x) = f sin x dx = [cos.x dx = (arctan x)': = [f(x) g(x)] = ==dx =

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Q: Evaluate the integral.  integral sin 3  x cos 5x dx

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Q: Find integral.

A: The given integral ∫cosxsinx dx can be evaluated as, Put, cosx=t Taking differential on both sides,…

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

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Q: Evaluate the definite integral. ∫0 π/2  Cos x Sin (Sinx) dx

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Q: sin x dy Given: y = Compute for dx 1-2 cos x

A: The given function is y=sin x1-2 cos x

Q: dy = sin(x+4) dx

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Q: S sin 8x sin x dx O - 0. 02 O - 0. 01 O 0.02 0.01 O O O

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Q: 11) (y)* = (In tanx)(x*)(sin x)* %3D

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Q: sin x dx V2-cos² x

A: Given : ∫(sin x/√2 - cos2 x) dx     ....(1)   Let cos x = t   Differentiating both sides w.r.t. x -…

Q: 11) (/y)* = (In tanx)(x*)(sin x)* %3D

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Q: / sin(In |x|) cos(In |æ|) + dx COS -

A: We have to prove that the given integral is true.

Q: ( sin (In 2x) - cos (in 2x))? +x dx 2x

A: Let's find.

Q: 4. sinx 1-sin² x dx

A: We have to find the value of the given integral ∫sinx1-sin2xdx

Q: integral of cos x sin^3 2 x dx

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Q: Q! O show th at [x sin'x + V1-x²] = sin'x sin x

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Q: Evaluate the integral sin x dx (2 + 3 cos x)2

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Q: Show that sin x dx=1-cos t (0<x<t<}r).

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Q: (d) sin (x )+tan dx – In +y = 0

A: We have to solve given problem:

Q: Q3: dy\dx of f(x)= tan x cot x is

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Q: a) | sin x dx Ssin'xe x+1 dx b) + 2x

A: We will use the double angle formula C=integrating constant

Q: Find dy and simplify whenever possible. dx sec x+tan x 1. у 3 sec x-tan x 2. у 3 е * соs e * — sin e…

A:

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

A: Antiderivative of sin^2(x) + 2sin(x) is given by,  ∫[ sin2x + 2sinx ]dx =∫sin2x dx + ∫2sinx dx

Q: [sin(In x) + cos(In x)]* dx 3. xp: 3x/10 In(3x) – (In(3x))²

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Q: find dy/dx. ƒ(x) = x3 sin x cos x

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Q: Calculate the integral (sec(x)+ tan(x))² dx.

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Q: the integral of tan^2 (x) cos^3 (x)dx

A: To evaluate the given trigonometric integral

Q: Prove dx dx 1 f ( sec -x+tan –I 2 1 | f (cosecz) %3D Vsin r sin x

A: Apply trigonometric properties to prove the result.

Q: Find the trigonometric integral ∫sin x cos4 x dx

A: Consider the integrals: ∫sinx·cos4xdx…

Q: Find dy and simplify whenever possible. dx secx+tan x 1. у %3 sec x-tan x - 2. y = e-* cos e¯* – sin…

A: 1. y=secx+tanxsecx-tanx2. y=e-x cose-x-sine-x3. y=arctanx-1+x2

Q: |x sin x dx 3. Pe* dx Je*sin x dx 4. 2.

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Q: Evaluate the integral.  integral sin 3  x cos 2 x dx

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Q: Find the trigonometric integral ∫sin2(x/2)  dx

A: From the given data:

Q: cos x -dx Compute the integral 1+(sin x)²

A: replace sinx=u cosxdx=du limits of u will be 0 to 1

Q: proximation at z = 0 to sin(4r) is A + Bx where A is:

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Q: Evaluate the integral. 2 sin -1 x dx

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Q: Find dy/dx if a. y = (sin-1 x)2 b. y = sin-1 (1/ x) .

A: a.The given function is y = (sin–1 x)2.

Q: Find dx and simplify whenever possible. 1-cosh x 1. у 3D 1+cosh x 2. y = x tanh¯x + In V1 – x²

A:

Q: Find dy/dx if y = In (tan(x).3$ec(x) + /sin (x³)

A: given,