Question 7 Estimate the error if T9 (trapeziod rule with n = 9) was used to calculate cos(4 x) dx . a) olerror| < 2.266 b) Oerror < 2.472 c) Olerror| < 2.06 d) O error < 1.854 e) Olerror| < 1.648

Q: 3. Evaluate fe cos rdr 4. Evaluate: / tan -1 (3x)dx.

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Q: 4-If y= cos 8t , find the frequency (w) and the fundamental period(T.) 5-If: y = (sinx+1) (cosx+1)'…

A: We know that, The fundamental period(T0) of cos(x) = 2.pi                            if cos(ax) = (…

Q: Question 9 Find n so that T, (trapeziod rule with n subintervals) is guaranteed to approximate |…

A: ∫05cos(2x) dx       to within 0.01We have to calculate for the n

Q: Question 3 Use the trapezoidal rule with n = 5 to approximate %3D 2 cos(x) dx. Keep at least two…

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Q: 5х, 5x sin°(cos* () dx 5 4 6 6

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Q: i) Find sin 6x+ cos 4x dx. 3 ii) Evaluate || et -dx . Hence, solve 2e* dx . (* +2)" +2

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Q: Question 3 4. a) Integrate tan (0) sec (0)d0.

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Q: 2. S tane sec4 0 d0

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Q: QUESTION 4 Solve the following integral by using substitution method. S(6- sin3x)' cos 3x dx.

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Q: */10 S sin(10z) arctan(sin 5x)dr = ? a)10(7 – 2) - 2 b)- 5 ) 5 (т — 2) T - 2 d)- 10 Ол - 10

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Q: luating√√9-x² dx using trigonometric substitution will lead to: **/2 sin²0d0 3 of th 9[*/ cos²0de…

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Q: Find sin(2x), cos(2x), and tan(2x) from the given information. sec(x) = 6, x in Quadrant IV %3D…

A: Given, sec(x) = 6,    x in 4th quadrant

Q: 7/2 S 3 cos (x) sin°(æ) dx =

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Q: Question 8 If we have to check the DE Sin(x) +y cos(x) =1 for Exact then M,--- dx -cos(x) sin(x)…

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Q: Question 6 |5x sinx dx = 5x cosr +5 sinx +c OA. 5x cosx -5 sinx +c В. OB. -5x cosx +5 sinx +c Oc.…

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Q: S 3. sin°ydy 1+ cosy

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Q: Question 7 Estimate the error if T7 (trapeziod rule with n = 7) was used to calculate cos(2 x) dx .…

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Q: Find sinif sec 0 II in nim 5 Find cosif sec 0 = 4

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Q: Find sin(2x), cos(2x),and tan(2x) from given information. sec (x)=6 , x in Quadrant IV • sin(2x) =…

A: As per the given data we have: sec(x)=6    ⇒    cos(x)=16

Q: 1. S sina de cos²x

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Q: 3 .3 S sin 2xcos 2xdx

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

Q: Question 2 Evaluate x cos(3x) dx. .2 x° CoS Question 3 Evaluate e" cos (2x) dx. Question 4 Evaluate…

A: According to the guidelines issued by the company We are supposed to answer only one question.…

Q: 4 5 Points ntegral of sin-cos-sin0 de has the form (e) +C. What should be the value of e =0?

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Q: Evaluete " 2X Cos(sin --

A: Use the inverse trigonometric identities and simplify.

Q: /2 S sin50cos3ed0

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Q: 6) If sin 0 = 0.2774, find cos 0. Round to four decimal places.

A: Given: sinθ=0.2774

Q: 9. Express tan 0 in terms of sec 0 for 0 in Quadrant II.

A: We know that, sec2θ=1+tan2θ So sec2θ=1+tan2θtan2θ=sec2θ-1tanθ=±sec2θ-1 But given that θ lie in…

Q: QUESTION 18 Compute the following. |-8sin (x) +18csc (2x)cot(2x) dx

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Q: rea of the region between the sine curve

A: Here we have to find the area of the region bounded by the sine curve and the x-axis from π2 to 2π.…

Q: cos[arccos(−0.1)]

A: Consider the given expression as coscos-1-0.1

Q: 2. cos(arctan(1)) =

A: cosarc cosx =x

Q: 3. S sin³ 0 cos³ 0 d0

A: Given

Q: 10) To Graph of y = cos2x b =D %3D 2 Period = Period = %3D Find the intervals below 1-

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Q: f/² () sin cos (sin (²) dx (Consider initially the first 2 terms)

A: To evaluate: ∫0π2sinx3cos4x3sin2x3dx Let I = ∫0π2sinx3cos4x3sin2x3dx We know that  sinxcosy =…

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

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Q: 2 sin(30) cos(30x) dx

A: Given integral is ∫0π2sin30cos30xdx

Q: 5- ft2 cost dt n/2 6- sin? 20 cos 20 de

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Q: 6. S cos32x sin*2xdx

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Q: The velocity of a particle moving along a line is ;2 – 2t sin(r2) meters per second. Then, the net…

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Q: 5. (1+ cos 3x ) dx

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Q: In=5 dx Sin^ (x) ( ategrate by parts for findu the Yreduction form (11) by using (i) find In and…

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Q: (12) ſ sin²x cos²x dx sin4x sin4x 8. 4 16 Option 1 Option 2 sin2x - 8. Option 3

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Q: ♫♫¹⁄² sin (*) cos (*) sin (²) dx (Consider initially the first 2 terms)

A: Solving the definite integral.

Q: 4. sin ||

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Q: Part 2. Use the integration techniques to solve for the antl-denV 1. 3p? tan p dp Integration by…

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Q: Question 7: Use the trapezoidal rule with 6 intervals to evaluate f* 10 x7 dx ,giving the answer…

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Q: Verify.

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Q: Evaluate 1) S sin ³x cos³x dx

A: Given: ∫sin3(x)cos3(x) dx

Q: Suppose that 3π/2≤θ≤2π,  csc(θ)=11/4, find sin(θ)=______. (round to 3 decimal places)

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