If the approximated value of , 16x³ dx using Simpson's rule is 260.03, then the error in the approximation is O a. 0.09 O b. 0.07 O c. 0.04 O d. 0.03

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Q: Given that 3 ex dx — ез . e, use this result to evaluate 5ex 6 dx.

A: Given that

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Q: 5 (2) (-2%) e dx %3D

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Q: Given that dr = ln a, find the exact value of a. V16 + 9x V9+ 4x?

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Q: 2. S 22+3x dx = 4 ( +c In 8.

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Q: For what value of kik>0, does (4kx-5k) dx =9k Select one: O 4 O 6 O 5 O 1 O 3 O 8

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Q: 3 Given that 3. e dx = e° - e, use this result to evaluate 3ex + 4 dx.

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Q: If x dx = 1, what is the value of a? %3D D. O 0.707 O 0.794 O 0.874 O 1.145 1.442 0 0

A: We can find the value of a as below.

Q: What is ſ e2x dx? 1+ex

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Q: . The value of e*dx by using 2-segment Simpson's 1/3 rule most nearly is 0.2 A. 7.8036 B. 7.8423 C.…

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A: Given  ∫016ex2dx

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A: Given the differential equation

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Q: Evaluate the given | coth - dx. 3 dz.

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Q: d Suppose a e R, where a > 0, a ± 1, what is - dz

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Q: Determine how large the number a has to be so that 08. 1 dx

A: Solution is given below

Q: d Suppose a E R, where a > 0, a ± 1, what is- - [a*]? dx

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Q: Hence, the work done is equal to the following. 5/4 W = 20/3x dx

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Q: Apply the open Newton-Cotes formula with 3.5 xe*dx n=1 to approximate 0.5

A: For n =1 , ∆x = b-a3 , and the abscissas are x0 = a+∆x and x1 = a+2∆x . The Lagrange polynomials…

Q: Given that 1 -dx + dr = ln a, find the exact value of a. V16+9x² V9+4x* 1.

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Q: x² dx 4

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A: We have to evaluate ∫-11x-52lnx+5dx using the two-point Gaussian quadrature formula. Now, the…

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Q: et dx 5-e

A: Given integral is

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Q: What is the value of a so that In (e* ) dx = 6 ? a A.) O В.) 1 С.) 2 D.) 3

A: Given: ∫a4ln(ex)dx=6

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A: We have to find error.

Q: The integral 2N | 6xe- dx can be done with the substitution u = and du = dx.

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Q: Show thet Pmle) Palx) dx = o for -1 Note: Legendre equotion ll-x) Pm Lx) -2x Pim lx) + mlmeD Pm…

A: Give :  Legendre Polynomials for m≠n To  find : ∫-11Pmx  Pnx dx =0

Q: d = e*, we must have that fe'dx = e*. Since dle)=e", %3D

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Q: S 3* e*dx

A: Integration means addition it is used for adding continuous function which can't be added by simple…

Q: 4. Describe in detail three separate ways to find /. Evaluate any two of these to show that they are…

A: I=∫x9-x2 dxUsing substitution method:u=9-x2du=-2x dxx dx=-du2=∫x9-x2  dx=∫-1u du2=-12∫duu=-12∫u-12…

Q: If IN = frNe-2= dx, show that IN +IN-1, and hence evaluate f r*e-2" dx = -

A: As per bartleby instruction when more then one question is given only one has to be answered. Please…

Q: 9. For what value of k, k> 0, does (4kx-5k) dx = k² O 1 O 2 3 O 4

A: On solving this we will get

Q: d Suppose a E R, where a > 0, a ± 1, what is[a*]? dx

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Q: Determine how large the number a has to be so that 00 dx

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Q: Evaluate using substitution and then integration by parts 1111 1121 36. x³ e** dx ete

A: ∫x3ex2dxSubstitute u=x2→dudx=2x→dx=12xdu=12∫ueuduIntegrate by parts:∫fg'=fg-∫f'gf=u and g'=euf'=1…

Q: While evaluating the approximate value of | 2² dx, using Trapezoidal rule, taking h = 0.5, the value…

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Q: Q1: what is on (3x) SI2 dx x2

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Q: 3 Given that ex dx = e³ – e, use this result to evaluate 7ex + 4 dx.

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Q: Without using a calculator, determine d/dx{2e^3x *cosh 4x−e^7x} in simplest terms.

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Q: Given that 1 -dr+ 1 - dx = ln a, find the exact value of a. V16+9x? V9+4x?

A: given: ∫01116+9x2dx+∫0219+4x2dx=lna we have to find the exact value of a.

Q: Evaluate the given integral: cIn 3 e dx. 1+ezz

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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.