Show that sin x dx=1-cos t (0

Q: Find the intergration of x^3(x^4-sine)^5 dx

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Q: Integrate: So a sin(x²) dx

A: We have to integrate

Q: If Sin-'x= Iny, show %3D ( l-xx) day - dx d X 2 x dy =y

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Q: Evaluate the integral. sin 4x cos 9x dx |sin 4x cos 9x dx =

A: topic - indefinite integral

Q: 28. The derivative of In(x sin x) is 1. 1 + cotx а. b. C. d. tan x +x - +x sinx

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Q: Integral of sin^3 x dx over cos^4 x

A: In this question we have to find the Integration.

Q: Integral of Sin^2(2t)cos^2(2t)dt

A: Given: ∫sin22tcos22tdt

Q: 7/3 x tan (x) dx 2

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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: If y- sinhx then prove that = dx

A: Fundamental inverse Trigonometric Identities: →cosh2y - sinh2y = 1 Basic derivative:…

Q: Integral from 0 to 2pi of sin(2x) dx

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Q: Compute integral. sin(x) cos(x)V4+sin? (x) dx. 2.

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Q: find integral tan 3 x dx

A: To find the integral of tan2x first split tan into two part and the using property of sec and tan…

Q: cos (In z) sin (In x) dx

A: To Evaluate the integral

Q: Integral from 0 to pi/2 of (cosx) /(sinx) ^(1/2) dx

A: we have to find definite integral of f(x) in [0,pi/2]

Q: 9.) JE sin°(x)cos*(x)dx 11.) F sin°(x)cos²(x)dx 2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 1. If f(x) = sinx, show that f(x + y)-f(x) = cos x siny - 2 sin x sin² 2 2Y-T

A: 1) Given f(x)=sin(x)

Q: Integrate (three) of th 1) f sin6x cos3x dx

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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: Compute integral sin(cos(x^2)) sin(x^2)x dx

A: Explanation is given below...

Q: Find the solution of (tan x – sin æsiny) dæ +cos xcosydy = 0

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Q: )if x+tany+ sin-x+ In(yx) +3**1 =4 then find y'

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Q: (A) Prove that: cosh x + sinh x = e*

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

A: Let's find.

Q: Find integration + dx Cos (x-1)

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Q: find integral sec 3 x dx

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Q: Determine dy/dx given that: y = sinx - sin³ x O cos³x O cos x sin² x O sin³ x O - cos³ x -

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Q: 3. J sin53x dx. 4. J tan 2x sec22x dx.

A: ∫ax+bn dx=1aax+bn+1n+1+C

Q: Find the indefinite integral ∫sec2 (x/2) tan (x/2) dx

A: Given: I=∫sec2x2tanx2dx

Q: FInd the length of the curve y= 2ln ( sin(x/2)) from x = π/5 to x = π

A: Formula to find the length of the curve is  ∫ab1+dydx2dxGiven y=2ln(sinx2) Lets find out dy/dx by…

Q: Consider sin °x cos2x dx. f we let 4=cos x, the integrand can be transformed to

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Q: Use sin 0 = 0, sin = 1, and sin t = 0 to estimate sinl E) (Round your answer to three decimal…

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Q: 4. Ify =/sin x+ /sin x+.to inf inity, dy _ cosx dx 2y-1 prove that

A: Derivative of Sinx is Cosx

Q: Integrate (three) of th 1) f sin6x cos3x dx 4) [x² (1+¹)4 dx

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Q: IT Evaluate the integral: (cos x + sin x cosx)dx

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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: The value of function f(x) = sin x (1 + cos x) is maximum when x is equal to

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Q: sinx f(x) = on [0, 2n] cos x-V2

A: Given :         f(x) = sin xcos x - 2 on 0, 2π   To determine the extrema of the above function…

Q: Find all extreme values for y=x+sinx^2 over [0,π]

A: Given,  y = x + sin2x  We have to find the extreme value in the interval 0, π

Q: Evaluate sin (4x) cos -2(4x) dx. | sin (4x) cos -2(4x) dx = O

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Q: 37. cos 6x dx 40. sin x? dx 39. cos do 42. tan x sec² x dx 41. sin 2x cos 2x dx csc2 x dx cot x sin…

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Q: Show that ∫∞−∞ sin x dx diverges.

A: To Show: ∫-∞∞sinxdx diverges.

Q: 3 cos x Evaluate | dx by using substit ution method. (1+sin x)“

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Q: In (sinh x ), + tanh x j + 1-x k )dx 1- sinx

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Q: 1 Integrate: S tan*÷x dx 3

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Q: Show that Sx cos*x dx = (x² + x sin 2x +cos 2x) + c

A: Given: ∫xcos2x dx=14x2+xsin2x+12cos2x+C.

Q: find integral tan 6 x sec  4 x dx

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Q: dz 5 – 2x cos 2x dx 1 + sin 2x sec² 0 de. tan 0

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Q: Compute f sin(cos(x²)) sin(x²)x dx

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