2. Integrate the following function (a) analytically 3. I- fxe2* dx and numerically using n = 4 (b) Trapezoid Rule (c) Simpson's Rule. Compute the percent error for both numerical integrations using the analytical value as the true value.

Q: Suppose f has absolute minimum value  m and absolutemaximum value M . Between what two values must…

A: Given that the absolute minimum value of f(x) is  m and absolute maximum value is M So,…

Q: Find the Integration of: fn (3sint + esin t) cost dt In 3

A: Given that, ⇒                   y =∫π2π( 3sint +esint) costln3dt⇒                     find the value…

Q: Apply the method of integration by parts to (In=) In æ ) (--) e dx dv

A:

Q: 1- Use trapezium's Rule with n = 4 to approximate the integral Vx dx

A: We have to use formula of Trapezoid Rule.

Q: What value of b > -1 maximizes the integral function

A: Given,

Q: dx 3. J TxVx-1

A: the given integral is: ∫dxxx-1 we have to evaluate the given integral.

Q: If the change of variables u = x -2 is used to evaluate the definite integral f(x) dx, what are the…

A:

Q: (b) Use Romberg integration to compute dx 1+x correct to three decimal places.

A: Given: I=∫01 dx1+x  correct to 3 deecimal placesLet h=0.25,…

Q: 24/ Answer two from the following :- 2-x - Evaluate and change the order of integration in 1 = ²*xy…

A: We have to solve the given problem.

Q: Q8 Integrate by parts: x sin x dx

A: .

Q: 6) dx X 3 Type 2 mproper integral 1-

A: We use Type II improper integral  Here at x=0 f(x) is discontinuous so we break the limit at x=0 If…

Q: If the change of the variables u=x^2-7 is used to to evaluate the definite integral upper 6 and…

A: Explanation of the answer is as follows

Q: 3) a) Use Simpson's rule with n=4. b) Estimate the error in the approximation. -2x dx jedx to…

A: Given integral is ∫06e−2xdx. a We have to approximate the given integral by using Simpson rule.…

Q: 1 to evaluate Vx - x dx. 8. (a) Use the substitution x = (b) Apply the integration by parts…

A:

Q: Verify the power rule for integration fx'dx= n+1

A: Given a power rule of integration,

Q: If the change of variables u = x2 - 4 is used to evaluate the definiteintegral, what are the new…

A: ∫24fx dx Here the lower limit is x=2 & upper limit is x=4.

Q: Q3) Reversing the order of integration 2 y² sinxy dy dx

A: Explanation of the solution is given below...

Q: (4) Find the integration by applying (by part method) Sin-¹y dy

A:

Q: 5. Evaluate S (tan(2y) + cot(2y))² dy using integration by algebraic substitution.

A:

Q: dx (2tx +x+ cos t) + (-sin x +t² +t)- = 0. dt %3D

A:

Q: In integrating the function fx' In Sx dx using integration by parts, what would you choose for your…

A:

Q: S°(xe* + 1)dx

A: In this question we have to solve the given integral by using some of the newton-cotes rule.

Q: 3. Use properties of integration to evaluate S, x³Vx* + 5dx. If necessary, round your answer to four…

A: Given : ∫12x3x4+5dx   The Answer:   13.5895

Q: Please determine the approximate integration using excel. ⌠13 (e0.5x + sin2x)dx, use n=4

A: Let,I=∫13e0.5x+sin2xdxI=e0.5x0.5+-cos2x2+CI=2e0.5x-cos2x2+C

Q: Q3] Use the trapezoidal rule of integration to determine the value of S, xlnx dx with h = 0.1, work…

A:

Q: Find the results of S Va² + x² dx and f va? – x² dx integrations

A:

Q: Suppose the side length of a cube is measured to be 5 cm with an accuracy of 0.1 cm. Use…

A:

Q: 6. f In² x dx

A: Topic = Integration

Q: In² xdx

A:

Q: 4. Evaluate e*dx using integration by parts.

A: Explanation and solutions is given below.....

Q: 2. se integration by pacts to eval integralig x² In (3x)dx niz

A:

Q: What are the new limits of integration if apply the substitution u = 7x + a to the integral sin (7x…

A:

Q: Determine the approximate integration using simple & modified trapezoidal, 1/3 Simpson's and3/8…

A: ∫13e0.5x + sin2x dx, use n = 4a = 1, b = 3so, h = b - an = 3 - 14 = 0.5            xo        xo +…

Q: d) Evaluate using integration by parts: [(x+2)ln x dx

A: Integration by parts rule:

Q: What is the result of the following ? integration dx Vx 4

A:

Q: Evaluate the definity integral  from 0-4 (x-3)(x-5)dx

A: Evaluate the integral ∫04x-3x-5 dx.

Q: 9. If the change of variables u =x- 2 is used to evaluate the definite integral f(x) dx, what are…

A:

Q: First make a substitution and then use integration by parts to evaluate the integr 36 e dx

A:

Q: 3. Change the order of integration and evaluate L dydx ex log y 2

A: Please see the explanation below

Q: The most convenient way to evaluate A) True B False 2x-3 S- -dx is use Integration by Parts. x²-3x+5

A:

Q: 1. Evaluate LL vsin(a*) dx dy by first changing the order of integration.

A:

Q: : Evaluate fxe dx to using Romberg integration to an error of order

A:

Q: 2. Determine the values of ʼn and h required to approximate fx²sin (-x) dx to within 10% using the…

A:

Q: What is the (a). general solution to xydx-(x+2) dy=0? (b) integrate.

A:

Q: The most convenient way to evaluate A True B False S 2x-3 x²-3x+5 -dx is use Integration by Parts.

A:

Q: ⌠13(e0.5x+sin2x)dx, use n=4

A: We will answer the first question as you didn't mention any. Please resubmit the other question…

Q: If the change of variables u = x² +1 is used to evaluate the definite integral f(x) dx, what are the…

A: given:- u = x^2 + 1 to find:- new limits.

Q: Solve numerically the integral e**dx ´dx by: (1) Trapezoidal rule with n = 4 (ii) Simpson's rule…

A: The given integral is, 12π∫-22e-x2dx

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.