18) sin 3 dt t

Q: 2. 1= j tan(4x³) ,sec²(4x²)xdx dx 1- I=31-2x) (In( 5. I= 3. 1= ftan? (3x) sec? (3x)dx

A: Here we have to find the value of the following integrations. Note :   As per our company guidelines…

Q: evaluate the integrals

A: since you have posted multiple questions , so I'll solve first one for you, for rest question's…

Q: 7. Prove: sin(t) dt sin(1) + cos(1) 4

A:

Q: 8. If r = sin (ƒ(t)), ƒ(0) = pai/3, and ƒ′(0) = 4, then what is dr/dtat t = 0?

A: Chain Rule d(f(g(x))dx   =   f'(g(x)) . g'(x) We have given r = sin(f(t))        f(0) =  π3  ,…

Q: tan(v) In(cos(v))dv.

A: Assume lncosv = t Differentiate both sides

Q: 3. [(3t +r*)sin (21)dt /

A:

Q: 2 sin? 11. y = 3x 2x2 12. y = cos°V2x – 1 3. 13. у %3D Vtan(х?)

A: As we know that; The chain rule: fgx'=f'gx·g'x The Quotient rule: fg'=f'·g-g'·fg2 The Power rule:…

Q: 5х, 5x sin°(cos* () dx 5 4 6 6

A:

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

A: Use trigonometric substitution method for solving the integral.

Q: Evaluate dy/dx at the point (π/2, π/2), if 2 sin^2 x + 1/2 cos y = (3 sin x)^11 . Mention all…

A:

Q: 5. If y= tan x, prove that y``=2(1+ y² )(3+ y²).

A: Prove the given equation

Q: (1+cos(4t) dt 2

A: Let's find integration of given function.

Q: 6) Find (cor dy of

A:

Q: sin (21 + 1) dt J cos² (21 + 1)

A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: 8. -dt 1+64t 2 sin-8 B. А. (). -1 2 tan 2 tan- 8 O c. D.

A:

Q: cos(t) dt 2/3sqrt(x+5)^5-10(x+5)^(1/2) +C (5 sin(t) + 9)2

A:

Q: 3 .3 S sin 2xcos 2xdx

A: The objective is to solve the integration ∫sin32xcos32xdx Let, 2x=t⇒dx=12dt, then…

Q: Show that - if W= cos (メ+y)+ Sin(メ-y) Wメメ Wyy ニ

A:

Q: S cos(3z)sin1º(3z) dz C 1 (cos (3z))10 + C 3. (sin(3z))10 + C D 1 (cos (3z))1 + C 33 (sin(3z))'l + C…

A: Topic = Integration

Q: 25. y = 2 cos yA 2 28. y = 2 sin ) -2TT -2 31. y = 3 sin (2x) (A)

A: In this, the amplitude is multiplied by 2 and x is scaled by 1/2.

Q: (§5.4, Q42) Calculate So™ f(x) dx, where sin x, x T

A:

Q: 2. +4y= sin(3t), y(0)=2, y'(0) = 0

A:

Q: Evaluate the integral. sin (8t + 16) dt cos (8t + 16) sin (8t + 16) dt = cos (8t + 16)

A: Solved below

Q: 1 -~-² ( 5 (52² + 4) = = = √( ² ) 6' +4' sin2t.dt

A: As per the instruction, we will be answering the first question. For (1), We need to verify the…

Q: Compute e4 cos (r – 3) dr with two decimal places. Number

A:

Q: T Use Wallis' formula: sinº (1) cos² (1) dx

A: Follow the procedure given below.

Q: 4 + cos t -dt 1 – sin t

A:

Q: 7. Evaluate t' sin(2t“) dt .

A:

Q: (3 cos t – 1)i + (2 sin t + 3)j,

A: We sketch the curve as

Q: 3) z = sin(ej³) + sinh(5230°)

A: We have evaluate the given complex number z=sinej3+sinh5∠30°

Q: 13. (2х + 1) sin 4x dx; и — 2х + 1, dv %3D sin 4x d 14. х cos 4x dx; и %3D х, dv 3D сos 4x dx

A: 13:      ∫(2x+1) sin4x dx                14:      ∫x cos4x dx

Q: .3 4 cos³ 4y /sin 4y dy

A: To find out the integration.

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

A: Recall the property of definite integral:

Q: 7/4 *(1 – sin 2t)3/2 cos 2t dt

A:

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

A:

Q: 21) (1 + cos 9t) 2 sin 9t dt

A:

Q: 8. 4 6° sin°3ycos *3y dy

A:

Q: sin 2t cos 2t dt 1 +3 cos 4t

A: Integration is the process of finding the anti-derivative function of the given function. The…

Q: 3 1-sin' t -dt 2 sin? t

A: To evaluate the integral∫1-sin3tsin2tdt

Q: 1. dz (1² + 5)² 2. COs z dz 3. sin 3r cos 5z de

A: Given: I1=∫x3x2+52dx, I2=∫excosxdx, I3=∫sin3xcos5xdx

Q: 11 csc²(3x) cot(3x) dx =, (Use Substitution Method) 11 11 +C 6 sin (3z) 6 11 11 +C 6 sin (3z) 6 11…

A:

Q: Evaluate the integral. sin (6t + 17) -dt CoS 2 (6t + 17) sin (6t + 17) dt%3D cos 2 (6t + 17)

A:

Q: 26. /(х, у) — х 27. f(х, у) — sin y 28. /(х, у) — х1 + 9у2

A: fx,y=x fx,y=siny fx,y=x2+9y2

Q: •7/3 (5 sec t tan + (4 tan t)j + (3sin t cos t) dt | -п/6

A: Solution

Q: Q# (17' Compute: [tan (10x)sec(10x)dx tan³ 1 tan(10x)+C 10 1 A) tan (10x) – 3 30 1 1 В) sec (10x)--…

A: We use substitution method to solve the Integral.

Q: 8. dr Cos dr |I+ sinr 9. 13 10. VH + 16 dt

A:

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.