4. S sin(tan-1 t) -dt 1+t2

Q: s sin(3x) + cos(5x) – sin sin)ax |dx

A:

Q: 26) If y=sin(-0).find dy d0

A: Given.

Q: 4 b. [√x ln xdx, 1 4 ㅠ C. fx√4-xdx, d. fx sin (2x) dx. 0

A: Solve the following

Q: O. p. S sin 2x cos 3x dx 3dx /1 + 9x²

A:

Q: 7/4 Q6// S*x cos3 2x sin* 2x dx

A: we have,

Q: 18) e2x = sin(x + 3y)

A:

Q: Find dt 1- t2 sin (t)

A: Solve the integration

Q: 2 a) lím sin x+1

A:

Q: Compute d/dx  sin-1 (x/x+1)

A:

Q: 4x3 — 2х2 — х+5dx А. -2 TT 3 sin t 4 dt cos²t В.

A: Evaluate the integral using the second Fundamental theorem of calculus.…

Q: 4. J (cos x – sin x)²dx

A:

Q: Find the General and Particular solution of = 8 sin 4x ; y = 6 when x = 0 %3D dx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 4. Evalaute cos(x) sin(x) dx

A: Given:

Q: 1- d/dz [cosz] = -sin z

A:

Q: 5. Evaluate 0.1 sinx dx. 1. S, sin(x²) dx 2. S

A: Given the given integrals are (1) ∫01sinx2dx (2) ∫01sinxxdx Use Maclaurin series…

Q: Show that L{cos at} = S s² + a² Hence find L{sin 8t sin 6t}.

A:

Q: dt cos (2 sin 21) /1– 4r

A:

Q: 4. ["s 0 sinx + 2 cos x dx

A:

Q: L[if i sin√2t dt²

A:

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…

A:

Q: 11.) F sin (x)cos²(x)dx 2

A: Note:   As per our company policy we should answer only one question each time, so please repost the…

Q: 8. y = In(2e-t sin t)

A:

Q: dy 2 5. Find if y = sin (27t)+tan-(2Tt) dt

A:

Q: 1. [* sin' y cos' ydy 3

A:

Q: 5) S V2 + sin 3t · cos 3t dt

A:

Q: 4 + cos t -dt 1 – sin t

A:

Q: 9. cos (2t) dt 10. " sin?t cost dt /2 11. sin'x cos?x dx 12. (2 sin0)² d®

A:

Q: -31 cosh 2t 7. (a) 2e- sinh 3t (b)-

A:

Q: - Tt/2 2 cosx dx 1+ (sin x)2 -T/2

A: Using substitution: So the limits of the integration would be given by: And

Q: 3. S sin? (2t) cos³ (2t) dt 4. ſ tan³(3x)dx

A:

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

A:

Q: 4. J S (esc²a – co sec 0 tand) d0 - -

A: Explained below...

Q: 18. S sin xdx 2-cos² X

A: The given integral is: I=∫sinx2-cos2xdx    ...1 As we know the common integral; ∫11-x2dx=sin-1x+C

Q: 7. y" + y = 3 sin(2r) +t cos(2t)

A: The general solution of an ordinary differential equation of the form;…

Q: 4) Evaluate the following sin (x) -dx 1+ cos (x) 1 ex dx (4x³ + 7*)dx --

A: Consider the following integral: I=∫sinx1+cosxdx Substitute 1+cosx=t→-sinxdx=dt→sinxdx=-dt in I:…

Q: "+25y 4r sin(51) – 2e" cos(5t)

A:

Q: 3 Q19- if z =- 4x³y sin sin (x³y) əz find əx

A: We want to find partial derivative of the given function.

Q: (7 cos° t dt 2

A: ∫0π/2 cos9tdt ∫0π/2 cost(1-sin2t )4dt here lets substitute that sint = u du/dt = cost du = costdt…

Q: d²s dt2 sin 3t + cos 3t |

A: In this question, we need to find s.

Q: 1 Evaluate the equation /o x² sin (xy)dydx

A:

Q: 3) e4x = sin(3x + 4y)

A:

Q: 5.S Vsin 2x . cos2 x dx

A: Integration is a process of adding up infinitesimally small pieces of an area. There are mainly 2…

Q: Q1\ Differentiate the following 1)2xsin-13x x+1 2)y = In Vx-2 1 3)y = sin-1 2x

A:

Q: 9. [sin Ssin' cos–dx 3 3

A: (9) To evaluate ∫sin5x3cosx3dx Substitute sinx3=u and cosx3dx=3du. Therefore,…

Q: d. a) dt [8 sin 1 2t] = d. b) |7 cos s 1 5 dx d. 3u] = -1 c) 10 sec du

A:

Q: | 10(2 sin(x)) cos(x)dx if J Ax)dx = 13

A: