2. The suitable Trignometric substitution that solves fx(x-2) dx is (x-1)=sin 0 x-1)3sec0 (x-1)=tan 0 (x-2)=s sec O

Q: 1. (2x4-x3-2x+3) dx 2. (3-2x)2 dx 3. 3(x-1)(2-3x) dx 4. (5-5x+x5) dx 5. 1/3 ex dx 6. (x2-cos x)…

A: The integration is an anti derivative process. it is reverse of the process of differentiation. Here…

Q: Find the particular solution for: y' sin(2y) - cosx = 0, x =when y = 0 %3D 2

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Q: 11, 0-20² 2. 3. चं 5. T S cos 2x dx sin(²³) cos²(:-) / dx 2x-1 4x dx dx 6. 7. 8. S [² (x² + 0²³) dx…

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Q: 2 tan(4x-1)-3 cos² (4x-1) If we let u = 4x – 1 for the dx, what will be the resulting integrand?…

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Q: Find the particular solution for: y' sin(2y) – cosx = 0, x =when y = 0 %3D

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Q: Find dy/dx of y = cos^-1(2x) * sin^-1(2x)

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Q: Obtain the General Solution : • tan'ydy : sin xdx e • COS "x sinx dx o • (3t sinix) dx = sin 4x dy

A: Solve above differential equations.

Q: 7/4 2 sec(6x)dx sin(r In(x)) 13x 1

A: (b)

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Q: 3. Find d²y/dx² of y= x cos (5x) – sin² x/ |

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Q: sin (2t + 1) - dt cos? (2t + 1) 31.

A: Use trigonometric substitution method for solving the integral.

Q: Solve exact equation 2x -)dx + (2x cos(2xy) + 8e²")dy = 0 x² + 1 (2y cos(2ry) + with initial…

A: We will solve the problem.

Q: dy tan tan x = 0 dx coscos x +

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Q: .Find a reduction formula for ea* sin" x dx. Hence evaluate e* sin x dx. 3

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Q: Find y' in y=sin¹ (5x5+2x) + Tan-¹ (x²) 1 1 1+x² -(5x5+2x)² A. y' B. y' C. y' D. y' = = 25x¹+2…

A: Given:y=sin-1(5x5+2x)+tan-1(x2)       y'=dydx=dsin-1(5x5+2x)+tan-1(x2)dx…

Q: What substitution should be used to solve the integral x²dx 4-9x2 sinu=3x/2 O sec u =2x/3 O sec u…

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Q: 4- Find dy/dx for: d- y = /1+ sin³ (x5) e- y = 2(Va – 1)( f- y = cos³{sin(2x*)} x-2 x²+3x' %3D

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Q: 4 sin (2x) dx cos (2x)t4

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Q: Find the general solution to 2- ди u = xt + x cos t + t sin x. 3 - -

A: Given: 2∂u∂t-3∂u∂x-u=xt+x cos t+t sin x

Q: 7) {(1- sin° 31)- cos3t dt 8) | t in’ (5x)· sec´ (5x) dx

A: 7) I=∫1-sin2 3t·cos 3t dt  ……1

Q: (b) Show that 2t cos x and sin x = 1 + ? (c) Show that dt dx 1 +

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Q: 1 =dx = V81-(3x+5)? 2 3x+5 -tan- (***) + c 9 o 음sin-1 (3g5) +c 9 o tan-! (**5) +c o sin-l (초5) +c…

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

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Q: 1. S e sin 4x cos 4x dx 2. S dx Je-2x dx e 2x

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Q: 1. S cos (3 sin x)cos (4 sin x). cosxdx sec*x dx 2. Jtanx 3. Sr 6 tan*x dx 4. /2 sin5x dx

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Q: 19. -π/2 21. -π/4 23. [³5e* dx sin 0 de cos x dx sec² 0 do (2x secx tan x) dx 20. rπ/3 22. 24. [¹-dx

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Q: find dy/dx 4x -x 2x 23) y= Sin- +x².Sec 2-x + 2x.Sec) 2 (ans.: (2-2»N(2-x² - x* 4 4

A: To find the dy/dx means y' of the given function

Q: 3) Show how the substitution u = 2 x shows that - - t/2 -Tt/2 S sin"x dx = S? cos"x dx

A: Let u=π2-x Differentiating u w.r.t. x- dudx=-1du=-dx Considering left hand side of the given…

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Q: Cos 5x dx 3 +Sin 5x 1. 2. dx J16-9 (n x)²

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Q: 1. . Use the method of characteristics to solve the first order equation Uz – 2uy with u(x, x) =…

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Q: 4- Find dy/dx for y = 3[(sin-"(e-3x*)²

A: f(x) = 3arcsin2e-3x2f'(x) =ddx 3arcsin2e-3x2=ln(3)·…

Q: 1. S(tan -1) dp 2. sin2 B cos ß dB 3. S: xdx -7-8x-x

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Q: 9. tan 4x sec24xdx d. cos 5xsin 5xdx e. x sin(3x² +1)dx f. [x* cos(2x' +1)dx

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Q: 1. Evaluate f sin*(2x + 3)cos (2x + 3) dx sin(2x + 3) put = t 2. Evaluate f dx Put x2 + 5 = t x2+5…

A: Explanation of the solution is given below.....

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

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Q: Find and simplify the result whenever possible dx 1. y=x+sin2x 1. y = 4 1 sin' 5x 3 2. y sin5x - 3.…

A: Solving for the number 4:                                          4) y=3xcos(x3)-9 sin(x3)   To…

Q: 3. Show that: • T/2 sin" x dx • T/2 cos" x dx

A: Recall the property of definite integral:

Q: z sin(2- 32)+cos(2 - 3a)+c | 4x cos(2 – 3x) dx 4x cos(3 3r) dx Option 1 Option 2 |4 cos(3- 3z) dr…

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Q: Find the general solution 6. y"+4y' = sec2x Solution 6. y=c, +c, cos 2x+c, sin 2x+ 16 sin 2x -In(sec…

A: Given differential equation is y'''+4y'=sec2x We have to find the solution of the given differential…

Q: Q3- Find: 1- Sv2 + sin3x . cos3x dx. 2-5* dx x5-2x sin 2x 2 sin x 4- f cscx cot x dx 4 cos x 5- S 3+…

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Q: ,1 x² - 4x⁹+ A) True B False sin(x) (1+x²)² |dx=0

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Q: 2. Solve (sin y – 3x² + 5)dx + (y +x cos y)dy = 0. (Test for exactness and solve)

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Q: (1) ſ [ (x³ + 2 + 7 ) dx (3) cos³x dx (2) √ x³ (2) x3 e3x+1 dx (4) sin x sin 2x dx

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Q: Find [(1 - cos² t)dt]. dx A. sin²x B. -sin²x C. 1 - sin²x D. - cos²x

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Q: 1 dx cos² 2x 3. 4. x² sin (x³) dx S elnvx+1 dx 5.

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Q: 9. (2 sin x – 3 cos x) dx • T/2 - T/2 -

A: We use Trigonometry table for final answer  and cos(-x) = cos(x)  sin(-x) = -sin(x)

Q: 16. √(16-9x²) dx 17. dx/ (9x² + 4) 18. sin³ x cos x dx 19. f (secs x) dx/csc x 20. Stan² x dx

A: