1 Which of the following is equivalent to -dx 1+ cosx+ sinx after appropriate half-angle substitution is used? (A dz B) dz + zp- 2+27 D) none of these E dz

Q: 2. One of (a)-(c) is incorrect. Find and correct the mistake. (a) - sin(y³) = 2y cos(y?) (b) dx…

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Q: The appropriate trigonometric substitution for * dx is V3x-x 3 3 X ==+ sin 0 2 2 sec 0 4 2 O Option…

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Q: sec-(2y cos r) = x"

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Q: (s,+)=(-3,1) X=5?+2+? y= 6st a) 4s x sinly) + 6+x?coscy) at (-3,1) b.) 8tx Sincy) + 6sx? Coscy> at…

A: GIVEN  (s,t)=(-3,1) X=s2+2t2  Y=6st substituting the value of s,t for X and Y we have  X=(-3)2…

Q: (p² –1)cos[cosh (In r)]dr

A: In this question, we need to find the integral.

Q: z = 2e"žsinx – 3e*cos(y) Ве find: www a²z a2z (n az а) дхду"") дудх ,b) ду

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Q: The x² – 4 dx can only be evaluated using trigonometric substitution technique . A) True B False

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Q: [o,1] Find the sne exponsion of fla)=x+2 in in Sine Sinlntix), %3D 00 4-(-1)^ %3D •Sin (nTx) (c) Sin…

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Q: (10) The result of (D-3D D, +2D;)sin(x-2y) is

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Q: 10. 3 J√cos z sin ³ zdz COS

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Q: If u = e3x. du = 2 cos 2x dx then du = 3e* dx, v = sin 2x. Select one: True O False

A: Differentiate the equation u=e3x with respect to x.…

Q: 8 Find the anti denivapine Sfa) faa or © f la) = Cos ( 6x) 16 - Sin? ( 6x)

A: f(x) = cos(6x)16-sin2(6x) ⇒I=∫f(x) = ∫cos(6x)16-sin2(6x)dx Since dsinxdx=cosx, therefore:…

Q: 3. Find . a. y ( +2r + 10) cos(r)

A: Find the derivatives of the given functions. Use the derivative formulas:…

Q: Prove the left side equal to right side in the following: s2 (eice = (sin at + at cos ar] 1 L-1 (s²…

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Q: Q3) find the soluation of differention equation 2) y' sin 2x = y cos 2x

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Q: 1+cosx, dr r = 1-cosx' dx

A: Using derivative to find dr/dx

Q: a) By expanding sin (2x + x) and using double angle formulae, show that sin 3x = 3 sin x – 4 sin°x .…

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Q: Use symmetry to evaluate the followingintegrals.

A: The given integral is ∫-π4π4sec2xdx

Q: 8:54 1 3. If y = (5x)sin(3x) , then %3D dy %3D dx Type here to search

A: This question is related to differentiations. Solve in 2nd step.

Q: 2 7 O Use the Trapezoidal rule with n= 4 to approximate the value of sin (x² )dx.

A: Given  0∫2√π sin(x2)dx  Let f(x) = sin(x2 )  Approximately the value f(x) by using trapezoidal rule…

Q: Find 7'(t), given 7(t) - 4e 2t (3 sin(2t), ,4 cos(4t)). F'(t) =

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Q: x + 2y- z = 3 and x + 3y+z= an be evaluated by the following triple ntegral: 1-x 2-т-Зу dz dy dx. 42…

A: We have to choose the correct option from the given options according to the given information

Q: What is the general solution of sin z sin ydx + cos rcosydy 0? %3D

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Q: 3. If v = sin- (4) + tan-' (±), find the value of r + y. 4. If z= ear+by. f(ax – by), prove that b…

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Q: The value of the integral (s cos (r) dr is S COS Select one: O s(cos(2) – cos(0)) -

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Q: 14. Find a) esin 2xdxb) J vanyt dx, using the substitution x= 2 tane. 15, Find a) fxe"-dx b) dx…

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Q: We apply one of the Half-Angle Formulas to simplify the integral cos (5æ) da. VWhat is the resulting…

A: We know the identity  Cos(2x)= 2cos2(x)-1

Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

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Q: Which of the following is equivalent to u=-cost+v3 sint ? a) u = 2 cos t +- 1 b) u = – cos| t+ 2 3…

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Q: (c) Integrate sin"uelog (cosu) . Where n is 482

A: Integrate the sinnuelog(cosu). Where n=482

Q: (12,50 Puanlar) 3- Evaluate the integral 3x +2 dx. V5 - 22 a) – 2 arcsin V5a + 3/5- a? +C b)2…

A: Given: The integral is ∫3x+25-x2dx

Q: ered # tion Bi Q) choose one only 1. If (x + y)² = x² + y² prove that = - dx 2. If y = sin³ () cos³…

A: To find the differentiation of given functions.

Q: The integral dx (x²+4)² sec ³0 de sin ²0 de ° csc ³0 de ° Scos²0 do can be transformed to which of…

A: Here we have to transformed the given integral.

Q: dz Find a? sin(2y – 5z) =1+y cos(6zx)

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Q: which u-sub will help integrate this? A. u = dx 11 [arctan(x)]" dæ = [9 + 12 cos(x)]" B. u 9+ 9x2 C.…

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Q: 7) Determine an eq ,in (x) and (y) , and then find a) y sec 1t , x csc-1t b) y = (sin 0)* ,x = (cos…

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Q: 7a6(cos +i Si ) IF USE DE MOIURES TheoREM To Find Z. 23

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Q: Which of the following is equal to s v² cos (v³)dv ? A sin 1 8 jsin 1 O Option 1 Option 2 D. sin C.…

A: The solution is Option B 13sin(1)

Q: Solve the differenttal equat on 1y +dy_64=12x-50 Sin 2x dx? doe

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Q: 2Tt Prove that a" sinax cos bx dx = 0 0.

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Q: Determine dy/dx of = 3x(sin(2/2)) O None of the choices O 12/cos (2/2) + sin(2/2) 0-12 sin(22) + 3…

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Q: The value of 6 Jo° (4+ cos2x)dx is: 글(똥-0.5) 1 ( 47 4T 글(똥 +0.5) 3 None 글(품 + 0.5) 1 4 3

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Q: Q2) a) Find an® sec²y dy b) Is cos4xv2-stn4x dx = (2- sin4x) +Ctrue or false? show me

A: Use fundamental theorem of calculus for part (a)  For part (b) use substitution method

Q: 3) Show that y" +y = 0, given that y = 2 sin x + 3 cosx

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Q: sec ec-'(2y cos r) = x"

A: This is a problem of derivative of the given function. By using general formula of derivation we…

Q: Given, w=2iz - sin iz. Find i dz 2+ cos iz -2- cos iz -2+cos iz -2+cos z

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Q: 2. Is it possible to write sin (37x) as a linear combination of sin(2rx) and sin(Tx) for all values…

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Q: If sin-r= In y, show that UTM dy (1-2) = y. dr

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