3- dx for y x sinx is equal to: a)2x cosx b) 2x sinx + cosx 2x c)x cosx+ sinx 2x

Q: 19-x Evaluate ,* sin(x + y*) dy dx

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Q: Show that for n > 2, tan x sec"-2 п — n-2 T dx . sec" x dx sec"- п — 1 п — Use this to find sec x…

A: ∫sec4x dxWe need to find the integration by using the given formula.

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: (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: Differentiate. y = sec(e) tan(e) sin (8) y = cos(e)? 2

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Q: y = sin(x) at |0, 0, with four equally – spaced points

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Q: 4si 2xcos²x dx sin2xcos2x

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

Q: Prove that (arccsc x) dx d d %3D (csc-1 x) = %3D - dx Ju/Vu2-1

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Q: 2- Evaluate sin x dx usin i. Trapezoidal rule ii. Simp

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Q: If y = cos x + sin 2x, find the value of y” - y’ +3y

A: We will differentiate the given function.

Q: If y = tan¬1 xy and (x = 2, y = 3) y will be equal to?

A: If y=tan-1xy  and x=2, y=3 We need to find the y'. Formula for  y' is, y'=11+xy2×x=x1+xy2

Q: 4. y = tan(x + a), , where 2x

A: You are asked for multiple questions. As per our guideline we can do only one. Please repost others.

Q: In sec2(sin2y)dy dy can be evaluated by writing it as sec2y

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

A: First find the first and second derivative of the given function then simply put and simplyfy

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

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Q: prove that  d/ dx ( sec x) =sec x tan x

A: We have to prove ddxsecx=secx tanx We know that secx=1cosx So, we have to differentiate ddx1cosx…

Q: Show that if y = V1 + sin x then sin x

A: We can solve it by doing derivative and make the proof.

Q: rcosA 2. r sin 0 dz dr de

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Q: In y = C, sin 8x + C cosax + 9x²- 2

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Q: What is if z = x²y+sin(ry²)? %3D dz = 2xy + y? sin(xy') az = x² + 2ay cos(xy) 8z = 2xy + y cos(xy?).…

A: The given function is z=x2y+sinxy2

Q: dy/dx = sec(x)tan(x)

A: Given: dydx=sec(x) tan(x) if y=sec(x) tan(x)

Q: y = cev2z + Cze + C3 cos(v2x) + C4 sin(/2x) + Czev3z + Cge + c7 cos(/3x) + Cg sin(/3x)?

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Q: Let 5 sin x + 6 cos y = 6. dy dx d²y dx?

A: Given that 5 sin (x)+6 cos (y)=6 -(a)Our Aim is to find  (i) dydx and (ii) d2ydx2

Q: Let 6 sin x + 7 cos y = 7. dy (6cos(x)csc(y))/7 dx dy = dx2

A: Simply take the derivative of the whole expression with respect to x than simplify.

Q: Let 6 sin x +7 cos y = 7. dy (6cos(x)csc(y))/7 %D dx dy dx2

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Q: When evaluating ∫x sin x dx, explain how letting u = sin x and dv = x dx makes the solution more…

A: ∫x sinx dx

Q: (-1)*+1 bn x sin nx dx || n -ㅠ

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Q: Given that Sin<x cosx dx, the substitution. U = COSX COSX sinx coSX sinx

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Q: .3 Use Trigonometric Substitution to evaluate: dx 2 |1+4x²

A: This question is based on indefinite integral.

Q: 4. y = Ae bx are cosax + Bebx sinax, where a and b(lowercase) parameters. (not to be eliminated)

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Q: 3. f10x-sec(5x) tan(5x²)dx ans : sec(5x²) +c (VF). cot 4. dx ,note: Vx = xr ans : 2 In

A: ∫10x·sec(5x2)tan(5x2)dxlet u=sec(5x2)du=sec(5x2)tan(5x2)·10x  dxdx=dusec(5x2)tan(5x2)·10x Replace dx…

Q: Show that y / / + y = 0 given that y = 2 sin x + 3 cosx

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Q: Evaluate sin'y cosy dy. 2

A: This is a integration problem

Q: dx is equal to 1+cos x O - cotx + cscx +c O - tanx + cscx + c O - cotx + secx + c O cotx + cscx + c

A: We have to find the integration and also find the limit in the second question.

Q: Let 3 sin x + 7 cos y = 3. dy %3D dx d²y dx?

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Q: sin ydy (4 + cos y)²/3

A: We know that integration of xn is xn+1/n+1 +C. Here C is integral cosntant.       Here i attached…

Q: sE de = 6 - +- + arctan( )) +c %3D 1+ Vx

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Q: if z=ex( x cos y-y sin y ), show that  ∂2z/∂x2+∂2z/∂y2=0.

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Q: If y = tan-1 xy and (x = 2, y = 3) %3D %3D y will be equal to?

A: Given: y=tan-1xy To find y' at x=2 and y=3. Solution: Chain rule of differentiation states that:…

Q: Find y' and y". y = cos(x?) y' - -sin (x²) ( 2x) y" =

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Q: l6X-tan 3X, (- find openint & concav f(x)= 6-(seč 3x)3 3 sec?

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Q: Calculate c{fie*sin (t - v) du}

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

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Q: 8. fx,y) = sinx cos y

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Q: What is y = sin (xy)

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Q: Evaluate ∫ex cos3(ex) dx using tables after performing the substitution u = ex.

A: We have to evaluate the integral by substitution method: ∫ex cos3ex dx Substituting, u=ex…