Use the reduction formula in Example 6 to show that w/2 n -1 (w/2 J sin"x dx sin"-x dx where n > 2 is an integer.

Q: d -1 ) Prove that cos 1(x) : dx V1-1

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Q: Q2/a) Find the integral f tan5x dx cos³x b) Find the integral cos*x dx 1-sinx

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Q: Step by step

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Q: x sin 10x dx

A: Given: ∫xsin10xdx

Q: 211 211 sin mx sin nx dx = 2 [cos(m-n)x- cos(m+n)x]dx 0.

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Q: (a) Find dy/dx for 3 tan x – In x x2 (b) Find f"(x) for the following function: e" In(x**) f(x) = x…

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Q: (a) In(1– x) +xe? (b) 2х 2x 1-cos(x) (d) V1+x-1 Check and briefly explain how to avoid the loss of…

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Q: Which is the du in y= sin (x2-2x + 1)? x2-2x + 1

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Q: Write S, = E(-1)i-la; where i=1 in ai = (-1)–1 sin x dx. (i–1)ñ x Show that a; > 0 and (an) is…

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Q: Q1) Show that: (b) (cosx) = -sinx =1+* (a) (1+x) =1+6x %3! (e) (VF) = (d) v1+ tan x

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Determine ƒ such that (1, sin 1) is on the graph of f and e2z + 5e² + sin æ ifx 0

A: When derivative function is given, to find the actual function integrate the given derivative of the…

Q: To evaluate 3cos x=1 dr. the integrand can be transformed to 1-sin2x A.) S(3cos³x + csc?x)dx B.) 3…

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Q: Let F(x) = | sin(7t) dt. 0, Find the MacLaurin polynomial of degree 7 for F(x). 0.71 Use this…

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Q: The approximation of the integral f(x-1) cos(x-1) dx using two points Gaussian quadrature formula…

A: Given integral is ∫−11x−12cosx−1dx. We have to approximate the given integral by using two point…

Q: The integral A B C D S³ x dx x² + √√√x²-1-1 sec²0 de 1+tano sine de 1 + cose sece tane de sece - 1…

A: We have to solve above integral

Q: calculate L4 for f(x)=76 cos(x/2) over [2pi/4, 2pi/2]

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Q: Use the symmetry of the graphs of the sine and cosine functions as an aid in evaluating each…

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Q: Evaluate | e'(sin(1) + e*)°dt using an appropriate substitution.

A: Given : ∫etsin1+et9dt

Q: Find the absolute maximum and minimum of f(t) = -2cos2t + sin4t on  the interval [0,pi/4]

A: The given function is, f(t)=-2cos2t+sin4t and the given interval is, 0,π4. Obtain the value of the…

Q: bx + c Given tan 3 - In(x2 - 8x + 25) + 1 -dx %3D x2 - 8x + 25

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Q: d) f(x) – e) f(x) = sin [In (x² - 3x)] sin x f(x) = 1+COS X

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Q: The following DE sin(x) +y cos(x) = 1 can be written as: dx Cos(x) sin(x) None of These 1-cos(x).…

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Q: b. b-a Use the equation fte)dx = lim ** ) to evaluate the following definite integral. n-0k=1 2 |(2x…

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Q: What is the maximum value of y = cos(0) for values of 0 between -720° and 720? O A. -1 О в 1 O C.0…

A: Given that: y=cosθ     and θ between -720° and 720°

Q: Show that the formula gives the decomposition odd function. e* = cosh(x) + sinh(x) of the function…

A: Even function: Let fx is the real-valued function, where x is the real number, then, fx is an even…

Q: (B) The evaluation of f- -dx is (x*+3x2 +1)[tan-( In|tan"+5| + e -In tan-( +c (i) (ii) (iii) None of…

A: No antiderivative could be found within the given time limit, or all supported integration methods…

Q: The sin(5x + 2x) dx cos5xcos 2x is equal to 2 In(sec 5x) + 5In(sec2x) +C А. 10 In(sec 5x) +…

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Q: The integral O [se Ss S S sec²0 de 1+ tane sece tane de sece - 1 O x dx x²+√√x²-1-1 sine de 1+ cose…

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Q: Test the ff ODE for exactness and find the general solution of the DE. (2x + 3y) dx + (3x + 4y) dy –…

A: Let's find.

Q: The f xcos x² 1-sin x2 dx is

A: Given :

Q: Prove the following: d -1 arccos(x) dx V1- x2

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Q: 1. Evaluate 1 (a) [ In(2x + 2)dx (b) [ sec'3x tan 3x dx

A: (1)(a) Use the method of substitution to solve the definite integral.…

Q: Use the graph of sin x/cos x to find all values of x between x =0 and x = 4t f %3D true: a. sin…

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Q: 8) S dx it sinx + cos x a) in (1 + tan =) + c b) In (i - tan £) + c c) - In (1 + tan x) + o 2 d.)…

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Q: Evaluate x2 dx Select one: on O(sin (2r- 1) + 2(2 (2ain (r) + sin(2si To (stn(2 1I) 2(2r sin(2sin

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Q: 1.) Evaluate In 2 e*2arctan e* J (1+ e2x) sec(2arctan e*)' А.) -dx. ežr(1 – e*r)- (arcsin e 2x) cos²…

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

Q: sin 7Z „Find the residue of f (z)at z = 4 (z – 4)? Let f (z) =

A: Note:

Q: The phase shift of f (x) tan(2x – n) is : Oto the left n to the left On to the right Oto the right

A: The solution is given as

Q: Q2: Derive the reduction formulas of f sin"xcos™x dx? Using this solve the S sin*xcos³x dx.

A: Given: ∫sin4x cos5x dx

Q: Consider the functions h : R→R and g : R -R defined by h(x) = 72 (5 + arctan(sinh 4æ)), . g(x) = 144…

A: Using inverse trigonometric  function properties

Q: 7 (a² +b°) 1 Prove that : dx = ở (a sin x+ b° cos² x)' 4a’b?

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Q: tan(In x) 1. Evaluate: dx A. In cos(In x) + C c.tan?(In x) + C B. In sec(ln x) + C D. tan(In x)² + C

A: The given integral is ∫tan(ln x)xdx

Q: There is a unique point a between where the function f(x) = sin x + 2 Cos a and 4 changes its…

A: Given f(x)=sinx+12cos2x Find Concavity  and Find πa

Q: Q4 Evaluate: f(1- cos²4x) sin4x dx.

A: The given integral is: I=∫1-cos24xsin4xdx   As we know the Power rule. ∫xndx=xn+1n+1+C

Q: Write out Taylor's formula around 0 of degree three, f(x) = P3(x) + E3(x), for f(x) = = COs x.

A: Given that fx=cosx. To determine the Taylor's formula around 0 of degree three. That is, fx=P3x+E3x…

Q: The f sin x cos²xdx is x sin 4x {A} 16 64 sin 4x x {B} 16 16 O A B O - sin³2x 48 sin³2x 48 +C + C…

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Q: Prove that : n/2 1 dx (a'sin'x + b’cos'x 4a°b³

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Q: . Consider the function ƒ(x) = cos x − 3x + 1. Since ƒ (0)ƒ (²) < 0, ƒ(x) has a root in [o,]. If we…

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Q: Find the smallest value of t such that t>0 and sin(8t)– sin(3t) =0.

A: The given equation is sin8t - sin3t  = 0 or,  sin8t  = sin3t or,  sin8t  = sin(pi-3t) On comparing…