P H2) = 3 (13) flx)- Sin () (x3-3x6x-8) 1. (15) Cos x %3D f66)=Sinx. +cosx 18 sinseti (19) 20) f6)=Sinx- x

Q: Integrate sin^2(7x)-cos(x)

A:

Q: (b) Prove that : - 1) (coshx)2 – (sinhx)2 = 1 ,2) coshx- sinhx = e-*, 3) (cothx)? -1= (cschx)?

A: Given that  The following

Q: 1 cos(sec-x) dx 2/V3 xVx²-1

A: Let's find.

Q: 2cosx dx 2 5- fn 1+(sinx)? π

A:

Q: What is the integral of question 23 and why is the answer 0?

A: Let f(t)= t^4*tan t/(2+cos t)

Q: 4 f sin(5 – 6x) sin (6x – 4)dx -

A: Here limit are not given so we integrate only without using of limit.

Q: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

A:

Q: 4. X sin (x) dx VI-X 1-メ-

A: “Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Integrate |sin2x cos 3xdx

A:

Q: Ssin(x)cos(2x)sin(3x) dx O sin(6x) sin(2x) , sin(2x)cos(4x) 24 + 8 8 sin(3x)cos(3x) , sin(2x)cos(2x)…

A: We need to evaluate integral.

Q: aie of sin(4x)+8 cos(x)+2x2 cos(4x)+8x sin(4x)+.

A:

Q: S sin² 2xcos² 2xdx

A: This question is based on indefinite integral using Trigonometric formula.

Q: In( cosh(7x) + sinh(7x)) + In( cosh(7x) - sinh(7x) ) =

A:

Q: 7. The derivatives of the function f (x) = cos(3x²) that follow are incorrect. What misconception…

A: The differentiation of product two functions can be calculated by using the formula,…

Q: f6)= Sin () (x 3x26x-8) 1 CosX In Ceos x) | $66)=Sinx+t Cosx. sinsetl -6()=DSin -2053 2.

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Q: 9.) JE sin°(x)cos*(x)dx 11.) F sin°(x)cos²(x)dx 2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Cos 2x dx ) Sin*2× + 8 1.

A: Given ∫cos2xsin22x+8dx

Q: 4. Show that sinx can be approximated by x-x³/6 within 0.01 on the interval [-1,1].

A: see my solution

Q: 3. Prove that cosh (2x) = cosh²x + sinh²x %3D

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Q: Flnd * |(sin 5x cos 3x + cos 5x sin 3x) dx cos 8x cos 3x + 3 cos5x – + c 8 + c Option 3 Option 2 cos…

A:

Q: 2 | (sin³x cos x + sinxcosx)dx 7/2 π

A:

Q: (b) Prove that : - 1) (coshx)² – (sinhx)² = 1

A:

Q: π/2 sin3 (4 ) αθ - π/2

A: To evaluate the following integrals

Q: csch (2 sin2x)dx 1. 1– 4x²

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Q: 4 fcos 3x sin³ 3x dx

A:

Q: 3. J sin53x dx. 4. J tan 2x sec22x dx.

A: ∫ax+bn dx=1aax+bn+1n+1+C

Q: 4. y = √esinx + 2 5. y = 4x In 4x 6. xe = sin 5x - sin 3y

A:

Q: 23. cos (3z + 4) dz 25. sec2 (3x + 2) dx

A: A

Q: 2cosx dx 5- ? 2 1+(sinx)2

A:

Q: Evaluate: S 0 tan¬(0)d0 arctan(8)–0 Sarctan 0 + C 2 arctan(0) 0 zarctan 0 + C 2 arctan 0- 0…

A: Please refer the attached image for complete solution.

Q: Exercises to solve: 1. fx² In(x + 1) dx 2. (x2 + x – 2).cos4x. dx 3. Se-*sinxdx 4. S sinh2x.cosh5x…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2. Use integration by parts to solve for [x³c x³ cosx dx.

A:

Q: 2) [ tan' (-) sec" () dx , 3) | 3) T5x+4 dx, 1) sin-1x dx , tan () sec? V5x +4

A: Since the question contains multiple part we can solve only first 3 for you. If you want any…

Q: Number 17

A: First we break sin^3 x in sin^2x*sin x, and then we replace sin^2 x by 1-cos^2 x.THen in the next…

Q: 1. D² {Sin ² x 3 2. JD²-15² √2e²x3

A: Here D is the differential operator. D=d/dx

Q: Evaluate sin (4x) cos -2(4x) dx. | sin (4x) cos -2(4x) dx = O

A:

Q: 5. S sinxtanx-cosxtanx dx sinxsecx(sinx+cosx)-5

A: Dear student, as per our rule we can only solve one question in one session. Please post the other…

Q: 2. Differentiate y = /sin(x² + 3)cosx

A:

Q: 3T 2cosx dx 1+(sinx)2 2 a)2 tan-'sinx|| b) 2 In sinx| c)2 In(1 + (sinx)² 2

A: We know that integration of 1/(a2+x2) is (1/a) tan-1(x/a) +c. Here' c 'is constant. Here i attached…

Q: Find dy/dx if sin-(4y²) = 8x² – 5y3 Answer: Find dy/dx if tan- (xy²) = 3x² – 5y² Answer:

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Q: Integrate: S dx sin ³x cos6x

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Q: 2. S CoSx+sinx-1

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Q: 4. EVALVATE | sin4x vos5x dx

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Q: The integral of sin x³ dx is cos x + Option 1 cos³ x 3 + C cos x + Option 2 cos² x 2 + C

A: Given ∫(sinx)3dx=∫sin3xdx

Q: S secs/2 (금x) tans (글x) dzx

A:

Q: 3 1 Find: S 2x3 --+ sin(x) dx x2

A: Consider the integral

Q: 5x cos dx 2 x3 cos 9x dx X' COS

A:

Q: 1)fsin 4.xdx esc(2+3lnx) 6) dx 2)ſcos 2xdx 7)f sec (4x)dx 3) fx tan(2x +1dx 8)fx csc 3- dx 9)fx…

A:

Q: 5- y = 1+sin(4x2 + 2)

A: Note - As per our guidelines we will solve first question only and rest will reposted.  ddxxn =nxn-1…

Q: SVx² + 10x + 25 dx. (cos4*x – sin4*x)dx dx

A:

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.