4y" + 8y" - 7у' + 15у %3D0 A. y = c,e3* + e0.5x (c2 cos x + c3 sin x) B. y = ce3* + e*(c2 cos 0.5x + c3 sin 0.5x) C. y = ce-3* + e0.5* (c2 cos x + C3 sin x) D. y = ce-3* + e*(c2 cos 0.5x + C3 sin 0.5x)

Q: 9 NO ION If g(x) = [ cos t dt, find g '(x). %3D x10 -sin (x) -10x cos (x) COS 1 cos (x°) %3 10x9 cos…

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Q: Use a change of variables or Table toevaluate the following definite integrals.

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Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

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Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

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Q: Use a change of variables or Table toevaluate the following definite integrals.

A: Given:  Calculation:  Let ln(p) = u Differentiate both sides (1/p)dp = du Also the limit of…

Q: | cos(5x) sin(13x)dx = 1 sin(&x) ) sin(18x 4 6. OB. - 5 sin(5x) sin(13x) + 13 cos(5x) 1 cos(1&x)…

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Q: Obtain general solution   y¹ = cos²x cos y

A: Obtain general solution  y¹ = cos²x cos y

Q: y = In(cos 3x) %3D 1 (- sin 3x)(3) Cos 3x y' %3D y' = 1 (- sin 3x) cos 3x 1 y' = (3) sin 3x %3D -…

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Q: 1. Integrate: e3x cos(x) dx

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Q: 4. If y3 +x³ = sin y + sin x find. dx 3y²-cosy А. cos x-3x2 3y2-cos y В. - cos x-3x2 cos x-3x2 C.…

A: Given: y3+x3=siny+sinx To find: dydx=?

Q: Find where z = sin (x²) cos (y) COS © 6.x sin (x²) cos (y²) COS 2.x sin (2²) 2x cos 2.x sin (x²) cos…

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Q: Find the general solution of y'=cos²xcosy

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Q: 1 Evaluate [ (x³ +cos(3x))dx 2

A: The given integral is ∫x3+12cos3xdx.

Q: 1. * Sx² sin 2x dx -x²cos2x ¸ x sin 2x , cos 2x +C 8. –x²cos2x x sin 2x , cos 2x + C A 2 2 B…

A: To Find : ∫x2sin(2x)dx

Q: [10 sin(2x) cos(2x) √ cos²(2x)-5 dx O a. 5 (cos² (2x)-5) ³/5 + C 3 5 O b. -(cos² (2x)-5)³/2 + C OC.…

A: To evaluate the given integral.

Q: Ou = 20 · x, du = 5 · sin(5· x) dx %3D Ou = 20 · x dx, du = cos(5 · x) Ou = 5 · x, dv = 20 · cos(x)…

A: we use the rule of integration of uv dx.see 2nd and 3rd step.

Q: - / sin 8x cos 5x dx = 1/6 cos3x + 1/26 cos13x + C ) -1/6 cos3x + 1/26 cos13x + C ) -1/6 cos3x -…

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Q: 3+2cosx dx is equal to (2+3cosx) sin x 2 cosx 2+3cos x) 2+3sin x 2 cos x 2 sin x (d) 2+3cosx 2+3sin…

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Q: [ 2x sin (4x)dx O =cos (4x) + C -x² 4 2 sin (4x) + 8x cos (4x) + C sin (4x) – x cos (4x) + C ○중cos…

A: Integration by parts

Q: Compute[x² sin(2x)dx. A.- x² cos(2x)+ xsin(2x)+ cos(2x)+C 1 1 B. — — x² cos(2x)+ —…

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Q: One approach to evaluating 2 cos (2x)dx is to first rewrite it as cos(4x) + 1 dx а. cos(2x) – 1 dx…

A: This is the question of integration.

Q: 2 sin 2x dx Tcost x + 4 cos² x – 2

A: We will answer the first question since exact one was not specified. Please resubmit the question…

Q: Differentiate y=excos(x2): y'= A. excos(x2)-2xsin(x2) B. -2xexsin(x2) C. ex(cos(x2)-2xsin(x2))…

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Q: 21. Integrate x cos(2x² + 7)dx. sin (2x²+7) 4(x²+7) B. sin(2x²+7)+c A. +C C. D. 4 4 sin(2x² +7)+c…

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Q: sin In 4+tan cos-dx 4+tan-Icos- 2 1+ cos 2sin In4 4+ tan cos- dx A 1+cos 4+ tan-cos- 2sin-In 4+…

A: To rewrite the given integral so that the integral can be evaluated easily. ∫sin…

Q: Use Table to evaluate the following definite integrals.

A: Given: ∫0110xdx

Q: | -3x cos 4x dx A) - 16 3 cos 48 -x sin 4x + C 3 3 3 B) cos 4x -x sin 3x +C 16 3 cos 4x - 16 3 C) -…

A: To evaluate the given intgral.

Q: 2. Differentiate y os=1(-2x³ – 3)³ = cOs

A: From the given problem:   y=cos-1-2x3-33   As we know that:   cos-1x=-11-x2   So,…

Q: sin(6x) cos(4x) dx = sin (2x) sin (6x) (b) 글(s сов (2х) cos (6x) 2 o+( cos (2x) cos (10x) sin (2x)…

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Q: 3. On (-∞, ∞), three functions y₁ (x) = cos 2x, y₂(x) = sin² x, y³(x) = cos² x are linearly…

A: Note: As per the guidelines we are supposed to only one answer because this is not a subparts…

Q: Integrate with respect to x: sin(3x) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

A: We have to solve the following integral .

Q: V3 with 0 < x < 2n. 2 cos 2x cos x – sin 2x sin x - -

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Q: Use a change of variables or Table toevaluate the following definite integrals.

A: To evaluate: ∫0π2sin2θ cosθ dθ Solution: Let substitute t=sinθ dtdθ=cosθdt=cosθ dθ Limit will also…

Q: 15,0-20³²4 2. 3. चं 5. T cos 2x dx sin(³) cos²( :-) / dx 2x - 1 4x dx dx 6. 7. [² (x² + 0²³) dx (x -…

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Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: To integrate: ∫2x21-4x3dx. Let substitute t=1-4x3. dtdx=-12x2dt-12=x2dx Substituting the value,…

Q: 11. y = x² sin x + 2x cos x – 2 sin x 12. y = x² cos x 2x sin x – 2 cos x - -

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Q: (2) Show that y=x sinx is a solution to y"+y= 2 cos x.

A: To Show: y=x sinx is a solution to y''+y=2cosx

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: The given integral is ∫04p9+p2dp. Let x2=9+p2. This gives  2x dx=2p dpxdx=pdp. when p =0,  x=3. when…

Q: Г(x3 + 2х — 1) cos 4x dx A .3 13 x (3x² 13 sin 4x + 4 |cos 4x + C + - 4 32 16 128 B (x³ (3x² 13 |cos…

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Q: Integrate with respect to x: sin(3r) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

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Q: 6. S cos 4x cosx dx will yield B.금sin Sx + 등sin 3x +c А. sin 5x + sin 3x + C c. 글cos 5x-글cos 3x + C…

A: Note: As per company policy we should solve only one question. So kindly repost the other questions…

Q: Differentiate y= e*cos (x2): y' = A -e*sin(x²) e(cos(x²) – 2 xsin(x²)) e*cos(x?) – 2 xsin(x²) D -2…

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Q: Use a change of variables or Table toevaluate the following definite integrals.

A: Given, I=∫25325dxx25x2-1

Q: 6x² + 5x + 16 S x3 + 3x² + 2x + 6 5 Injx+31+ In (x² + 2)√2 tan ¹() + C Option 1 5 Injx +31+ In (x² +…

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Q: Find the solution of the equation zxx + zyy =e-xcos(y) which tends to zero as x-> ∞ and has the…

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Q: A particular solution for y +2y +y=1-cosX

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Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: Given     ∫(x+1)42xdx Formula ddx(xn )=nxn-1 ∫xndx=xn+1n+1+C

Q: Integrate f Osin-15x+C ○ -sin-¹5x + C 1 dx 1-25x2 - 5 H|K sin ¹5x + C cos ¹5x + C

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Q: + 5x* + 4 cos x)dx = et – x° + cos x + c et + x 4 sin x + c - 4e" + x° + 4 cos x + c ,5 4e" + x° + 4…

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