3 Estimate the error if S10 (Simpson's rule with n = 10) was used to calculate sin(4 x) dx .

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

A:

Q: 2x2sinh(x3)cosh?(x3) Option 3 O :The dy/dx for the y(x) = sinh?(x3) cosh ²(3x²) Option 1 O 6x2…

A: Solve for the given

Q: 14. S 5 sin 3x cos 3x dx 15. ſ tan? Ode

A: We can solve the given integral as follows:

Q: Estimate sinx? dx with an error of less than 0.001.

A: Given ∫01sin(x2)dx

Q: Use differentials (or equivalently, a linear approximation) to approximate sin(40°) as follows: Let…

A: Given, f(x)=y= sin 40° Therefore, f'(x)= y'= dy/dx= d(sin 40°)/dx f'(x)= cos 40°

Q: Q1\| Integrate SIX of the following functions: sinh(lnx)dx 1) 3) | sin?(2x).cos(3x) dx 2) ex. sinxdx

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Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is: = None of the choices

A:

Q: S cos*x sinx dx

A:

Q: S(sinx + cos x)² dx

A: To find: The integral of . Formula used: Algebraic formula: Trigonometric formula: Integration…

Q: 3. Evaluate dx. Hence find the value of sinx dx. Va -x)

A:

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

A: we have to find the most general antiderivative of the given integral and then we have to verify the…

Q: to determine the approximate value of v(1+x³)dx

A:

Q: sin(2t)dt 0,

A:

Q: Find dy/dx by implicit differentiation. (sin pix + cos piy)8 = 12

A:

Q: Find dy/dx for following functions. 1) y = csc-(e2lnx) + sin-1(2lnv3x)

A: it is given that,  y=csc-1e2lnx2+sin-1(2ln3x) we have to find dydx=?

Q: of the tangent line to the sine function at the origin. y y= sin(7 x) values with the number of…

A:

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: Find cosh² (t) sinh5 (t) dt.

A:

Q: B. Use the trapezium rule with 6 ordinates to estimate fe* dx correct to two decimal places.

A:

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

A:

Q: Use the trapezoidal rule with n = 2 to approximate the value of sin(x²)dx. Round your answer to four…

A:

Q: Find the length of the curve f(x) = ln(sin x), 0 ≤x ≤π/6.

A:

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

A:

Q: Find by implicit differentiation. dx 4 + 8x = sin(xy') dy Answer: dx

A: see below the calculation and steps below

Q: Find by implicit differentiation. 3+ 6z = sin(zy') dy Answer: dz

A: Solution is in step 2

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

A:

Q: Find dy/dx for following functions. 1) y = csc-(e2inx?) + sin-1(2lnv3x)

A:

Q: Q2]Using Simpsons1/3 rule for evaluation of sinh(e-*) dx use n = 4 andwork to 5 decimal place?

A:

Q: From the figure formed in integrating -dx, what is the term or value that is adjacent to the angle…

A: Given:    ∫x2-3xdx

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

A:

Q: Estimate the error if S3 (Simpson's rule with n= 8) was used to calculate sin(2x) dx . a) O lerror|…

A:

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

A: We have to find indefinite integration and we have to check it by differentiation: ∫-5 sin tdt We…

Q: Use the Euler method with dx = 0.5 to estimate y(5) if y′ = y2/sqrt(x) and y(1) =-1. What is the…

A: Consider the formula used in Euler’s method.Also summarize the given data in the question.

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

A: We have to find and check the answer by differentiation of the indefinite integral: ∫-sec2 x3dx…

Q: f sin-¹(x) dx

A:

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

A: Evaluate: ∫x2-1dx

Q: find the antiderivative of dx/sqrt(ex-1)

A: To find : The antiderivative of dxex-1 Solution The antiderivative can be evaluated as, ∫dxex-1 Put…

Q: 2 sin x f(x) = 1+2cosx 5. Pvaluated at x = 1 rad

A:

Q: find dy / dx for Hhe follo wing 2X y=3+ ln (sin x?)+In (sin 5x)

A:

Q: 16. S(3 sin 0 + 5 cos 0)d0

A: A detailed solution is given below     ( As per our guidelines, i have to answer only 1st question…

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

A:

Q: The actual error of the approximation of I = x² sin (x³) dx using composite Simpson's rule with n=4…

A:

Q: Find dy/dx by implicit differentiation. 11 11 dy/dx = (Express your answer using positive exponents…

A: The given function is 11x3+11y3=7

Q: Find the derivative of the function. y = 6 In sin 22x O A. 24 sin 2x OB. 12 In sin 2x C. 24 cot 2x O…

A: We can find the derivative on the given function by using the chain  rule of differentiation.

Q: Q/ Find to the following functions: dx 1- sinh (x² + 7x + 12) 2- cosh²(17 – 4x²)

A:

Q: •4 Estimate the error if S6 (Simpson's rule with n= 6) was used to calculate sin(2 x) dx . a) O…

A:

Q: S sin(v3x + 2}dx

A: To evaluate the given integral

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.