1. Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x +5y dx cos? x + 1. r tan-

Q: 1. Given y= [In(3x² +8)] dy find tan(6x) dx

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Q: - Evaluate sin x dx using 3 i. Trapezoidal rule ii. Simpson's rule iii. Simpson's rule, taking n = 6

A: We have to evaluate ∫0π2sin x dx. Here a=0 and b=π2=1.570796 Given n=6 ∴ h = b-an = 1.570796-06 =…

Q: Recall that cos- arccos x. Find r1/2 e sin(cosx) dx. 0.

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Q: 3. Given the equation y = In(cos(x)): What is dx/dy? secx -seox -tanx -cotx None of the choices.

A: I am attaching image so that you understand each and every step.

Q: Find dy/dx for the following : 1) y = x + sin x² + sin-1 5x

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

Q: Find dy/dx for the following functi 5" + 5*y = In sin-1 e*

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Q: H 2= x? tan y/ at (lo1) %3D Ex by

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Q: for the following function: Find dx 1- y = sin-1 V2x + 3 2- y = 3cot(cosx)

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

Q: 4- Find dy/dx for: a- y = sec?x – tan?x b- y = sec³ ( – x) %3D c- y = sin(tan(3x)) d- y = /1+ sin³…

A: NOTE- Since questions 1, 2, 3, 5 and 6 are incomplete, so solving question 4 only. Please submit the…

Q: + b¬ + cx = 0 dt lution given by: - (A sin ßx + B cos ß.

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Q: d e) (In|sin x)) dx

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Q: d) y = sin*(x'/3) + arctan(r?)

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Q: 1 is 1 H.W Find y' for y = ecosx * tan-1(5x) * (5x² + 1) ?

A: for y , y'=?

Q: Consider solving dx using a suitable trigonometric substitution. After performing substitution with…

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Q: 1/2 Evaluate I = dx correct to 3 decimal places using Romberg's method. sin x %3D

A: Here A is the sum of the first and last value  B is the sum of other values

Q: a) Given that y= sinh'(cos(x)), provide detailed derivation to obtain the expression of dx

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Q: The equation Can be using the mne thod of Separation of Varia bles dy Sin(x+y) |3D And the output is…

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Q: TT sin 5. Approximate dx by Simpson's rule with seventh ordinates?

A: Simpson's Rule:    ∫abf(x)dx=∆x3f(x0)+4f(x1)+2f(x2)+...+2f(xn-2)+4(fn-1)+f(xn) Where, ∆x=b-an We…

Q: The result of dy/dx for the following function is COS X y = 1+sin x

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Q: 4 Find dy/dx for: y = sec?x- tan²x b- y = sec -x) C- y = sin(tan(3x))

A: It is asked to differentiate the following functions with respect to x: a) y=sec2x-tan2x b)…

Q: 2- Find dy/dx for y = In(tan(2x2))

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Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. tan2y dy = sin3x dx

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Q: Hw) if J-0- Gso and X=O+ Cas e Show that Sece+tan 0

A: The given differentiation can be solved by using chain rule. Initially, the y expression can be…

Q: Compute for the arcsinx dx . Which of the following is not an antiderivative of the function f(0) =…

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Q: I) Find the volume of the solid obtained by rotating the sine function between x -0 and x x about…

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Q: Can you help me step by step?

A: Given: -

Q: Use the Errors in the Trapezoidal Rule and Simpson's Rule cos(4nx) dx

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Q: a)- Find for, (x+ y)* = tan-14× + T* + InIny dy dx

A: To find dy/dx.

Q: Demonstrate and derive the following Bernoulli's Equation. - 2y tan x = y² tan²x dx

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Q: The integral I com S f se fse x dx x² + √√√x²-1. cose de 1-sin sinᎾ dᎾ 1+ cose sec²0 de 1+ tane sece…

A: Substitute x= secθ and solve . dsecθdθ = sec(θ) tan(θ).

Q: The appropriate change of variables for the dx is Vx²-4 x=2 cosØ O x=2 sec Ø O x=2tan Ø O x=2 sineØ

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Q: dx 5) prove that sin x+c using method of trigonometric substitution. %3D

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Q: Solve the equation for x, where x is restricted to the given interval. y = 3 tan 2x - 1, for x in…

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Q: Let x = 0.46 and y = 4.74. Determine the value of C when you ev |tan-(2x)dx.(Use 2 decimal digit)

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Q: dx 6. S; ezx+1

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Q: find dy for ee Sin (メ+34) dx

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Q: 4) Given y = 3 sin 2x, Find the Amplitude Interval and Period (n2, 0) (0. 0) Amplitude interval =…

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Q: find dy /dx for the following 3 2 -1 Y3x'+Sin x+ Sin5X

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Q: 4- Find dy/dx for: a- y = sec?x- tan?x b- y = sec - x) c- y = sin(tan(3x))

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Q: at (x = })? dy Csc(3x) Sin(3x) + Cos(x), Find Let y =

A: The given function is: y=csc(3x)sin(3x)+cos(x)  =csc2(3x)+cos(x) To find the derivative of it:…

Q: 2- Evaluate sin x dx using i. Trapezoidal rule ii. Simpson's rule iii. Simpson's rule, taking n = 6

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Q: In Va? + b² dx In x arc tan- Jo (x + a)² + b² where a and b are real.

A: We will prove the given identity by solving the integral using appropriate substitution.

Q: (b) Evaluate the given trigonometric integral sin r dx (x² + 1)(x² + 9)

A: The given integral is ∫-∞∞sinx(x2+1)(x2+9)dx. It is of the form ∫-∞∞f(x)g(x)sin(nx)dx. To solve this…

Q: Find dy/dx for the following 1) y = x3 + sin x? + sin-1 5x

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Consider the implicit function. ev = sin (2x) dy in terms of x. dx Determine the formula for dy dx

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Q: If y= cot"+ tan-1x?), then dy dx x2 Select one: 2х + 1+x*' 1-x4 2x O a. 2x O b. 1+x' 1+x? 2x Oc. 2x…

A: All given options are wrong. See the attachment

Q: Find a/dx2 at the given point without eliminating the parameter. *=0+ cos0 and y =1+sin ; 0 =n/6

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Q: B) Find and It x sin 3z and y= tan 3z dx

A: x=sin23xy=tan 3xWe need to find dydx and d2ydx2.

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.