Q: 1. Find the value of the following integral: sin vi dx using Simpson's rule when n = 8.

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) e40…

A: We have to find

Q: Use the table of integrals at the back of the text to evaluate the integrals ∫sin t/3 sin t/6 dt

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Q: Evaluate the integral. |sin° (x)cos“ (x)dx

A: In this question, the exponent of cos(x) is even i.e. 4, and the exponent of sin(x) is odd i.e 5,…

Q: 9. For the integral 8 sin" (x)cos(x)dx, if we use the substitution u = sin(x), what will be 3 the…

A: Topic - integration by substitution

Q: sin? x dx

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Q: dy 1 Let u = tan-y sin y – cos y -

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Q: I. Evaluate the following integrals. Check by differentiation. S sin 50 cos 50d0

A: Given;            ∫sin 5θ cos 5θ dθ Apply u-substitution: u=cos 5θ⇒du=-5 sin 5θ dθ            =∫-u5…

Q: Approximate the following integrals using the Trapezoidal rule. r0.35 2 dx x2-4 1. 2. Sfx sin(x) dx…

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Q: I = S(1+ sin x)³ cos x dx

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Q: Which of the following integrals are improper? Why?  integral 0 to 1  tan x dx

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Q: y=sin

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Q: sin(6x) Vi? +4 dt 7

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Q: sin x dx e lme

A:

Q: Consider the following integrals 00 4 sin? x i. dx x² + 6 e9t dt ii. e9t – 1 Mark the correct one…

A: Given: i.∫1∞4 sin2xx2+6dx ii.∫01e9t dte9t-1

Q: What is the area under one crest of the sine curve, from x = O to x = n? y=sin x dx 1/2

A: Given problem:-

Q: 2. Evaluate the Trigonometric integral. C (a). S sin(2x) cosxdx. rT/2 (b). S cot?xcsc*xdx. T/4

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Q: dx When evaluating the definite integral / Te why must you 16 – x2" choose the antiderivative–coth…

A: Given:              ∫68dx16-x2 why must you choose the antiderivative 14coth-1x4 rather than…

Q: valuate the following Integrals 1 -3 +1 dx 4secx tan x- 2 sec? x)dx .3 dx x² +1

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Q: find formulas for the functions represented by the integrals.

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Q: 12 Which expression represents the trapezoidal approximation T3 to the integral sin (V7) dx?

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Q: In the following equation/s, find the indefinite integral :-   see the equation attached here

A: We have to calculate the given integral   the given integral is

Q: Use the substitution x = 3 sin t to evaluate the integral f V9 – x² dx. | Note: Use C for an…

A: Given; I=∫9-x2dx   ...1   Use the trigonometric identity; 1). sin2x+cos2x=1 2). cos2x=2cos2x-1 And…

Q: Q2 - Evaluate the following integrals i. S cosx sin*x dx

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Q: Evaluate the following integrals S, sin () cos" () dx ) dx

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Q: cost sin², dt sin´t+sint – 6

A: Given - A function To Find - Integrate the function

Q: In the following equation/s, find the indefinite integral :- see the equation attached here .

A: Given: ∫t2t3+1 dt

Q: Integrate the following integrals using either integration by parts or integration by substitution.…

A: I=∫e-2θsin6θ dθ Integrating by parts, we get I=∫e-2θsin6θ dθ=e-2θ∫sin6θ dθ-∫de-2θdθ×∫sin6θ…

Q: Q: Find the integral for the following functions: - sin(x). esec( x) 1) S cos (x) 2) S 3ln?(x) dx

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Q: 2 sin? t sec“ t dt

A: To determine:

Q: Find the values of the following Integrals: ii) S sinx tan'ccord dx ü) Sex uci+ e* ) dze in) St…

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Q: b) sec* 0 d0 Give the exact answer.

A: The given integral is ∫π4π3sec4θ dθ

Q: Evaluate the integral. (Use C for the constant of integration.) 4 sin Vx xp

A: To evaluate the given integral.

Q: s) Calculate the indefinite integral using Trigonometric Substitution. X [ dx +x²

A: This is a problem related to integral. Based on the trigonometric substitution we will answer the…

Q: Evaluate the following integral.

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Q: 2 Find the definite integral fo5 tan(x)dx using strips of width for the trapezium rule correct to…

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Q: Using an appropriate substitution, the integral f e cos(e* + 1) dx is equal to:

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Q: |/ (cos(x) + sin(x))² dx

A: *Used the (a+b)2= a2 + 2ab + b2 formula.

Q: Given 4 cos(x²) dx 2 How many Trapezoids will you need to estimate the definite integral to an…

A: Given the integral I=∫24cosx2dx. (a) We need an accuracy of 0.001 when the Trapezoidal rule. The…

Q: Use the substitution x = 3 sin t to evaluate the integral f v9 – x² dx. - Note: Use C for an…

A:

Q: For the given integral dx sin-cot- 2 2 what is u?

A: Take u=x/2 then integrate it

Q: Find the following integrals: sin x (i) [sin' x cos? x dx dx sin (x+ a) (ii)

A: In this question, we need to find the following integrals.

Q: The best substitution to use for the integral sin z V1+ cos z dx

A: when we substitute, u = 1 + cosx then the value of du = - sinx dx

Q: Find approximate value of the following integral by using the trapezoidal rul 10 " 10 sin(20x²)dx…

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Q: Which expression represents the midpoint approximation M3 to the integral r12 sin (/æ) dx?

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Q: To evaluate the integral | x sin(x2) dx we use the substitution O a. x= t O b. sinx =t O c. sin x2…

A: Explanation of the solution is given below....

Q: S. The resulting integral of sin cos-sino d0 has the form | 2 2 -F(0) + C. What should be the value…

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Q: sec{s)ds

A: We know, ∫abf(x) dx = ∫abf(a+b-x) dx

Q: (x+1)dx x²(x+1)?

A: Integrate above equation by partial fraction method.

Q: For ſ sin" (0) cos (0)d0, use a suitable change of variables to determine the indefinite integral.

A: Given : ∫sin7θcosθdθ

Q: What is the value of the integral f sin(6z) arctan(sin 3r)dr? a) 3(7 – 2) b) c) d) 6(* - 2) e) - 3

A: Let  I=∫0π6sin(6x)·tan-1sin3x dx =∫0π6(2sin3x·cos3x)tan-1sin3x dx   ∵sin2x=2sinx cosx Assume,…