11) Define A(k) = x dx Using area, create a nice formula for A(k). Explain your area reasoning. Using area, explain why f" sin(0) de = 0 Using area, explain why cos(0) de = 0

Q: Evaluate e sin x cos x dx using Simpson rule with h 20

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Q: Use Simpson's 1/3 rule with (n₁ = 2), and Simpson -2 1 estimate tan-¹(2). [Hint: tan-¹ (2) = ₁²; dxl

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

Q: Find the area bounded by the trigonometric curves y=sinx and y=cosx from; x== 3.459 square units…

A: Area bounded by the curve .

Q: Using an appropriate substitution, the integral cosxe+2 sinx) dx is equal to:

A: Solve intregal

Q: 10 Use aepropriate substitution Ond then a trigonometric oubtitution to evaleiate the integial. dx…

A: This question can be solved using the concept of integration by substitution.

Q: Use the trapezoidal rule with n = 5 to approximate 3 cos(x) -dx Keep at least 2 decimal places…

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Q: 2. Evaluate J dx (cos³x sin³x)

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Q: 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x= to 3.459 square units…

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Q: x3 V4 + x2 dx

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Q: S cose de 1-sine sece tane de sece - 1 The integral fo fse Si x dx x²+√√√x²−1−1 sino de 1+ cose…

A: we have to above integration

Q: Evaluate the Trigonometric Integral sin (x) cos /2 (x) dæ ,3) sin° (x) cos

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Q: Use the addition formulas for sinh x and cosh x to prove tanh u + tanh v tanh(u + v) = 1+ tanh u…

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Q: 10 Use Simpson's Rule with n = 8 to approximate f cosx dx. 2

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Q: Q3: Let cosh(x)3D5, x>0 , Find values of: sinh(x), tanh(x).coth x ,sech x,csch x

A: Given, cosh(x)=5, x>0

Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x + 5…

A: The formula for Simpson's rule isSn=∆x3f(x0)+4f(x1)+2f(x2)+4f(x3)+...+4f(xn-1)+f(xn) where…

Q: Step 2 To find the integral x Cos Bx dx by the parts fomula, us sin , as Used in the previous step.…

A: Integration by parts ∫u.vdx=u∫vdx-∫dudx×∫vdxdx To find: ∫xcos8xdx

Q: x = -sin 2y x = cos y --

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Q: 8. Find the area enclosed by 1 leaf of r=sin30

A: Let's find.

Q: 1 Proof (I): (sinhx)' = Vx? +1

A: For direct Proof:

Q: sin ede 1- cos e 8.

A: The integral of sinθ is given by -cosθ and the integral of cosθ is given by sinθ. The basic formula…

Q: Use Simpson's rule with n = 6 to approximate %3D cos(a) dx 0.08 Keep at least 2 decimal places…

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Q: 4. sinx 1-sin² x dx

A: We have to find the value of the given integral ∫sinx1-sin2xdx

Q: Ni cos(2?)a. Cos | x dx

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Q: Given tanh(x)+ tanh ¯' (y) = 1, show that, 1- y? 1 – x² dy dx

A: Formula,ddxtanh-1x=11-x2Note- Since multiple questions are asked, I am answering the first question…

Q: Evaluate sin(x) · In ( cos(x)) dx using integration by parts.

A:

Q: | cos (5x) cos (3x)dx

A: Given integral: ∫cos5xcos3xdx We know, cosαcosβ=12cosα+β+cosα-β. Also, ∫cosxdx=sinx+c.

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral SIn(tan x)…

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Q: 91. Prove the integration formula tanx dx = In | secx| + C (a) by using algebra and integration by…

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Q: Prove the addition formula for cosh x given by cosh(x + y) = cosh x cosh y + sinh x sinh y.

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Q: Use integration by parts to find L[cos t]. Do not use et.

A: Laplace transform

Q: Find the si0pe of the given Function 1.) hlx) = sin x cos 3x at * = 3 メ 2.) y= In at メ = -2 メー! 3.)…

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Q: 6. In(x*y?) %3D х* +уз 7. У- Arccos(e2x)

A: Given In(x3y2)=x2+y3y=cos-1(e2x)we need to find the second derivative of the given equation

Q: Use sin 0 = 0, sin = 1, and sin t = 0 to estimate sinl E) (Round your answer to three decimal…

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Q: Evaluate the integral (exact value). e3x sin(6x) dx %3D

A: Integration By Parts Formula

Q: Evaluate 0, dx by dividing the interval into 10 equal parts 8х-5 by using Simpson's one - third…

A:

Q: Use integration tables to find or evaluate the integral ∫ 1 / sin   x cos   x dx

A: We have to evaluate the integral: ∫1sin x cos xdx We know the identity: sin2x+cos2x=1 Substituting…

Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is:

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Q: dr =ズ Sin )=s OP Type a a exact awser Using X as needed

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Q: Use Simpson's rule with n = 6 to approximate cos(a) dx Keep at least 2 decimal places accuracy in…

A: The solution is given below in the next step:

Q: Find the trigonometric integral ∫cos3( x − 1) dx

A: Find the trigonometric integral ∫cos3( x − 1) dx

Q: Find the trigonometric integral ∫sin x cos4 x dx

A: Consider the integrals: ∫sinx·cos4xdx…

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

A:

Q: Let I = S sin 2xdx be given. After substituting y = tan x, how can 5 cos? x+7 sin? x the integral I…

A: Given :

Q: Use the trapezoidal rule with n = 8 to approximate cos(x) -dx Keep at least 2 decimal places…

A:

Q: A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -pai to x =…

A: given

Q: Evaluate sin (x) e-x dx by use Simpson's rule. h=0.5

A:

Q: 39.) Show how to use (a) trapezoidal rule and (b) Simpsons rule with n=4 to 4 approximate ſ,"…

A: There are different methods of solving a definite integral without integrating it such as the…

Q: Use the Trapezoidal Rule with n = 10 to approximate the given integral. 20 6 cos (7x) dr Compare…

A: Given that

Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x +…

A: