Prove that Va2 + 4 sin ( sec %3D V2 +4

Q: | sin(6y) sin(8y) dy.

A: we have to solve the integral

Q: Show that J (x) = 2 sin x

A: By definition,                  . Now,  we need to prove the above statement by taking n = 1/2.

Q: 2 sin? 11. y = 3x 2x2 12. y = cos°V2x – 1 3. 13. у %3D Vtan(х?)

A: As we know that; The chain rule: fgx'=f'gx·g'x The Quotient rule: fg'=f'·g-g'·fg2 The Power rule:…

Q: 2. Evaluate the integral / sin'at dt

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Q: sen z + cos x dz | (tag z + 1) dx = In sec x+z + C 37. %3D cos 2

A: 37.   Given integral, ∫sen x+ cos xcos xdx

Q: Prove that x2 cos x dx = T(2 – n) (+ sin æ)?

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Q: find the volume of the solid

A: Find volume of solid.Sketch the given function.

Q: sin vx dx (4+cos2Vx) 4) J J (4+cos2V

A: Explanation of solution as follows:

Q: tan x dy +y sin x dr = 0, when x = 0, y = | O y (3- cos 21) = 2 O y (cos 2x O y° (2 – cos 2x) = 1…

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Q: リ=!-Cos2x 1+(os 2x prove y = 2 tanx .secx

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

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Q: Q. Use first principle rule and proue that if y=s %3D secl tand = secx

A: Given: y=secx We know that for any given functiony=fx, first derivative is given by…

Q: a) Differentiate f(x) = sin x from first principtes. %3D

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Q: 1 dy sin¬' x If y = xv1 – x² + sin=1 x, prove that 24 – 2

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Q: Siny+ tany siny %3D 1+ secy

A: Let's find.

Q: ... at verifies the identity. OC. B. sin 9x cos 7x - cos 9x sin 7x = sin (9x – 7x) = sin 2x sin 9x…

A: Given query is to find the correct option to prove the identity.

Q: 5. If y= tan x, prove that y``=2(1+ y² )(3+ y²).

A: Prove the given equation

Q: Find Domain and Range бяц tue Ⓒsin (x+3) +2y x²+2y 3x + y² 3) 3x + Sin (3x) +2y+Z² Ⓒ x+2y cos2x…

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Q: tan y dy + In (secy) In (6)sec® de

A: Given data:     The given integral is: . The given integral can be written as, Assume Let…

Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

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

Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

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Q: What is the integrable form of sin-cos-sin0 d0? 2 A /1 – u² du B Vu²-1 du © : fcomndn cosu du D sinu…

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Q: What is the integrable form of sin-cos-sin0 de? 2 2

A: A detailed solution is given below.

Q: What substitution should be used to solve the integral S O sin u=3x/2 O sec u =2x/3 O sec u =3x/2 O…

A: Evaluate the integral by using substitution method

Q: evaluate  0∫π 0∫1 1/6∫1/2 xy sin z dxdydz

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Q: d tanx = sec?x. dx Prove that sec² %3D

A: To prove the equation, we need to simplify the left hand side of the equation. According to the…

Q: 1. Solve the DE tan x sin y v + ( 3tan X -2 cos y) sec'x=0

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Q: ∞ sin2x dx (x²+1)²

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Q: Show that (i) | te 3 sint dt 50 -3t %3D

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Q: b) Is S cos4xv2 – sin4x dx = V(2 – sin4x)³ + C true or false? show me %3D

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Q: Use Property 8 to estimate the value of the integral.

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Q: The solution of the DE (1+ tan x)y'=-secx coty is O None of these siny + In cosx| = c %3D sinx +…

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Q: 2. Apply appropriate trigonometric substitution to compute the integral 1-4x +2 dx /2x

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Q: Evaluate the integral + tan sec dt

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Q: 2. Show that the LT of sin(wt) is L sin(wt)] (s) where w is a positive constant.

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Q: 4. Use definition (not tables) of L {f(t)}= [ e"f(t)dt to find L{sin(2t)} . %3D

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Q: What is the integrable form of sin-cos-sin0 de 2 2 du 2 1– u² du cosu du -2 sinu du

A: To write the integrable form.

Q: Find where w= cos z - cos x cos 2y + sin x sin 2y and z x+2y. Me.

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Q: The answer of integ ra Ssinzx cos3% dX

A: We have to evaluate the given integral.

Q: Show: 2 x + 2 sin dydx + 2y 1 va sin-dydx = 4 2y 2 va

A: The question is of change of order. First we need to identify the region formed by limits of…

Q: ди ди 1 x + y Jx + Jy IF u=cot show that x +- sin 2u=0 + ду 4

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Q: What is the integrable form of sin-cos-sine de? 2 2 V1-u? du -2 sinu du u² – 1 du 2/ cosu du

A: We have given integral Let, I=∫sinθ2cosθ2sinθdθ As, sin2x=2sinxcosx sinx=2sinx2cosx2 So,…

Q: Evaluate the integral. dx JSlx2 - 3 sin 1 33 x + C 3 sec1 |9x - 3| + C sec 1 19 x| +C * sec 13/5 x|…

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Q: 2 = sin5t constitute a fundamenta L

A: Y1=cos5t and y2=sin5t  do not a fundamental set of solutions of differential equations y"+16y=0

Q: cos' x dx

A:

Q: Verify that sin(x+y)+sin(x-y)=2sinxcosy

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Q: 4. Use definition (not tables) of L{f(t)}= [ e"f(t)dt to find L{sin(2t)} .

A: