Find the theoretical error bound in approximating SN" sin(x?) dx using Boole's Rule.

Q: S In(sin(x))dx

A: Given, I=∫lnsinx dx To evaluate I.

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

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Q: Find the exact value. In 3 0 ³ sech 4 x tanh x dx

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Q: Find the integral. er sin(5x)dx - IT

A: Known integral formula:

Q: (24) Evaluate the integral: | Va sin(1 + x/2)dx.

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Q: Solve Cauchy Euler DE 4x^2y"-4xy'+3y=sin ln(-x), x less than 0

A: Let t =-x >0. Then the differential equation       4x2y''-4xy'+3y=sinln-x becomes…

Q: 2. Evaluate the integral / sin'at dt

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Q: Integrate: So a sin(x²) dx

A: We have to integrate

Q: Evaluate the integral.

A:

Q: Use Simpson's rule with n = 4 to approximate cos(x) dx 1

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Q: Find the differential of z = sin²(5x) + ev

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Q: 2. Evaluate the integral: | sinh x cosh² x dx

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Q: Evaluate the integral.  integral sin 3  x cos 5x dx

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Q: Find integral of sin^2 (x/2) dx with bounds of 0 to pi

A: Find the integral of sin^2 (x/2) dx with the bounds 0 to π.

Q: Evaluate the definite integral. 1. S(sin(2x) – cos(2x)) dx

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Q: Evaluate S sinh x cosh x dx by letting u=cosh x

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Q: Find the indefinite integral. sinh(4 - 7x) dx

A: evaluate the indefinite integral ∫sinh4-7xdx

Q: The approximation of I cos (x²+5) dx using simple Simpson's rule is:

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Q: Find integration + dx Cos (x-1)

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Q: Evaluate the indefinite integral. sec* (x)dx

A: We have to find the integral of sec^4(x)  Please see the explanation below

Q: Evaluate the definite integral. sec (x/4) dx 0.

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Q: Evaluate the integral.

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Q: Find the indefinite integral ∫sinh 6x dx

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Q: Q4: To evaluate the integral cos x dx using the reduction formula of cosine function

A: We know that reduction formula for  ∫cosndx=1ncosn-1(x)sin(x)+n-1n∫cosn-2(x)dx Now we will solve…

Q: Lnx sin 2x dx

A: Use the properties of definite integral and solve the question.

Q: Find the indefinite integral. sinh(8 – 7x) dx

A: From the given problem: I=∫sinh8-7xdx  ....(1) As we know that; ∫sinhxdx=coshx+C

Q: Find the indefinite integral ∫sinh(1 − 2x) dx

A:

Q: Find the indefinite integral. sinh(4- 5x) dx

A: To find:∫sinh4-5xdx

Q: Verify the formulas by differentiation. ∫ 1/x + 1 dx = ln | x + 1 | + C, x ≠ -1

A: We have to verify by formulas of differentiation where expression is given as: ∫1x+1dx=lnx+1+C, x≠-1…

Q: Use Property 8 to estimate the value of the integral.

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Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your v?

A: Solution

Q: In integrating the function f(3x + 5)(cos ) dx using integration by parts, what would be your du?

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Q: Evaluate the integral.  integral sin 6  x cos 5x dx

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Q: Find the indefinite integral. ∫sec x/2 dx

A: Given ∫sec x/2 dx. We need to evaluate the above integral.

Q: S tanʼx dx

A: Answer is given in next step.

Q: Calculate the derivative e8x d In (t)dt dæ using Part 2 of the Fundamental Theorem of Calculus.…

A: Given To apply the fundamental theorem of calculus first simplify these integrals so that this…

Q: dy Find by implicit differentiation. dx 14 In x= 18 - In y dy dx (Type an exact answer.)

A: Consider the given expression 14ln x=18-ln y.

Q: calculate the integral.

A: Given integral is We will use the following substitution to evaluate the integral

Q: Evaluate the integral. sinh 5a -dx +C. 5x

A: Evaluate the integral the given function Sinh is hyperbole function.

Q: Evaluate the integral.

A: ∫cosh2(x)sinh(x)dx

Q: Evaluate integral 0 to pie sin 2 x cos 4 x dx

A: To Evaluate the integral given below:-I=∫0πsin2(x)cos4(x)dx

Q: Evaluate the integral.  integral sin 3  x cos 2 x dx

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Q: Show that ∫∞−∞ sin x dx diverges.

A: To Show: ∫-∞∞sinxdx diverges.

Q: 15)S (VA +) dx

A: We are authorized to solve only 1 question, please repost remaining questions

Q: Find the indefinite integral  ∫sin3 x cos2 x dx

A: We have to find the indefinite integral ∫sin3 x cos2 x dx

Q: Evaluate integral 0 to pie sin 2 x cos 3 x dx

A: Explanation: Given that,  ∫0πsin2xcos3xdx   Formula Used: Trig. identity:1-sin2x=cos2xSum rule of…

Q: arc sin z = -i log(iz + V1- 22).

A: