Example : Find S“ (cos ti + sin tj+ tk)dt

Q: sin (t) -dt 3 (4+ cos (t))?

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Q: At a certain moment, a race official is watching a race car approach the finish line along a…

A: At a certain moment, a race official is watching a race car approach the finish line along a…

Q: Show that A" cos (ах ah + b) = | 2 sin cos a + bx +n (ah + T 2

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Q: Evaluate the integrals

A: First of all use the trigonometric formula that is 1-sin2x=cos2x in the given integral to simplify…

Q: 5. Find the values of a and b such that dx tan 1 + sinx a + b . %3D

A: We need to integrate ∫11+sinxdx

Q: 4 sin' t cos tdt 4 sin"(t) cos (t) %3D

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Q: (a) Show that the equation cos rdr + (1+ -(+)- sin rdy = 0 is not exact.

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Q: Evaluate sin (3x) cos (6x) dx Select one: cos(9r) A cos(3r) tC 18

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Q: 5. " cos (w) sin* (;w) dw -2n

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: S sin° (3t) cos(3t)dt Evaluate COS

A: To determine the value of the integral.

Q: Eliminate the parameter: I = sin 3t, y = cos 3t, 0 <t <T/3. = COS

A: x= sin 3t     and y=cos 3t     for    0≤t≤π3 We need to eliminate the parameter i.e. we have to…

Q: 3 cos° tdt 5. 1+sint

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Q: Q/ ind dy if 24-sini' (xe!)=sin'(x*)+ cos (x")

A: Given that      2y - sin-1(x2+1) = sin2(x4) + cos2(x4) Here we have to find dy/dx.

Q: Differentiate cos cos" Vi-x? y = ecos

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Q: 40 a) Find sin' xcos' xdx by using substitution u = cosx.

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Q: Using the substitution u = cos(2x), S sin (2x) cos (2x) dx %3D

A: The given integral is ∫sin52xcos32xdx.

Q: (b) Differentiate y cos-1 23

A: Differentiate the given y with respect to x.

Q: derive 8t sin t (d) s %3D cos t t5

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Q: 0° S (c) Prove that: 2cos 20. cose 2 + 2 tan0. sin0 = %3D cos?e – sin? e cose o AEGW is drawn.

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Q: What is the general solution of sin z sin ydx + cos rcosydy 0? %3D

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Q: tanla= 2 with 3T LaL2p 3 2 and Sin lb) = 3 with IT L6LT 2. %3D

A: Solution:-  tana=-23   with 3π2&lt;a&lt;2π (fourth quadrant) sinb=34 with    π2&lt;b&lt;π   (second…

Q: The smallest positive number for which sin(t) - cos(2t) = 0 is t =

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Q: 2 f(t) = ( tv4t2 + 1, sin(t) cos² (t), t2 + 1

A: As you ask parts b and c. in part b we need to find the equation of the tangent line to the curve at…

Q: Evaluate f sin (3t) cos(3t)dt COS Select one: sin (3t) +C a. b. sin(3t) +C sin (3t) + C d. sin (3t)…

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Q: (3 cos t – 1)i + (2 sin t + 3)j,

A: We sketch the curve as

Q: O sin (z)cos(z)dz

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Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) Determine the…

A: We will use concept of arc length in 3d We want to determine the length of a vector function,…

Q: ) // Show that y + y = 0, given that y = 2 sin x + 3 cos.x

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Q: 5) coS I sin rdr

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Q: sin Tt cos Tt dt

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Q: find dr/ ds r cos 2s + sin2 s = π

A: It is given that,r cos2s+sin2s=πWe have to find drds

Q: 2 Convert r = to rectangular form. 7 sin 0 COS

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Q: (2 cos t, 2 sin t, t), where 0 <t < .

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Q: cos t dt 1 + sin t 37.

A: The given integral,37. ∫cos t1+sin tdt

Q: 2Tt Prove that a" sinax cos bx dx = 0 0.

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Q: Is this: sin x cos y- cos x sin y/ cos x sin y reciprocal quotient pythagoreom  algebra

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Q: /2 cos a sin(sin r) dx

A: using method of substitution

Q: What is the value of d. (sin x3 dx cos x²)? COS

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Q: Hf sin x = A + B cos 2x +C cos 4x, then A = %3D C =

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Q: 7. sin A = [ Select] %3D 8. cos A = [ Select ) 9. tan A = I Select)

A: Given,

Q: / tan( 4x + 3) dx Evaluate: (A) –In |cos (4x+ 3)|+C 4 B 4 ® -im [sin(4r + 3)| +C В –In |csc…

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Q: a sin a + In v ) da + tan adv = 0 Cos a

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Q: (11). - cos?(2y) sin? (x), y(등) =0 Workings y= tan '(z - 글sin 2v) +

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Q: Sketch X,(t) and Xa(t) Where X,() = - Sim3t Sin3t %3D 3. X,(e) = /a Sin 3t %3D

A: To draw the graph of functions X1(t)=-13sin3t and X2(t)=13sin3t, substitute different values of t in…

Q: Use the double-angle formula cos 2x = 2 cos x – 1 to evaluate the integral 1 1+ cos 2x dx

A: The given integral is ∫11+cos2xdx

Q: Cos Vt dt 3. Evaluate

A: The integration of the given integral is; Cos√t/√t.

Q: Differentiate  cos t sin t

A: We have to differentiate cos t sin t. Given function is: f(t) = cos t sin t Then we get,  ft=122 sin…

Q: 5. sin'(21) cos°(21) dt

A: