The upper bound of the error when using Trapezoidal rule to approximate the integral 5 S xe*dx is хе O a. 0.02442 O b. 0.03319 O C. 0.4211 O d. 0.11202 e. 0.8277

Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx.

A: Given integral is ∫03 x3+xdx Number of sub-intervals = 6 Take f(x) = x3+x Step size  ∆x  = 3-06…

Q: Find dr/d0. 10) e1/3 – r1/3 =1

A: Given query is to find the derivative.

Q: Sketch the graph of y = 4-√9-2² over the interval [-3, 3], and use the notion of net area to compute…

A: The given curve is:

Q: 9 dx Evaluate: J2 (1-3x)* Α. ο0 C. 0.008 В. О D. 0.0144

A:

Q: 4 (1+2 In x)* 6. J dx б.

A: We have to find

Q: 2 dx x3 - x

A: We will find the integral as following.

Q: Use Trapezoidal and Simpsons 1/3 rule to estimate integral ( - 2x° + 7x - 5) de.

A: The expression ∫13x3-2x2+7x-5dx. We have to use Trapezoidal and Simpsons 13 rule to estimate the…

Q: Use Trapezoidal Rule with (n- 4) to find the integral dx x-1

A:

Q: 12 What is the true error associated with estimating the integral (2x² + 4x + 4)dx by 7 using the…

A:

Q: The Area between k*x3 and k*sin (x) is 2. What is the value of k?

A:

Q: Use the Midpoint Rule to evaluate the integral Sx-dx.

A: Midpoint rule:Let f(x) is a polynomial of degree ⩽n-1Let the midpoint x1=a+b2 and…

Q: 16 Evaluate the integral f 2x (x2 + 7)º dx using the substitution u = x? + 7. %3D | 20 (2* + 7)" dz…

A: We need to evaluate the integral ∫2x(x2+7)16dx with the help of substitution. This can be evaluated…

Q: In x dx = n a, (a>0) 2a 23. Show that

A: Definite integration is the area of a region that is enclosed by the integrand. The function must be…

Q: c) Sa* sin*x dx

A: To evaluate : The integral  ∫π43π4 sin4 x dx .

Q: a) Estimate the following definite integral numerically by using Simpson's rule. Take n=4 steps.…

A: Sol:- Simpson's Rule Approximation∫abfxdx ≈Δ x3fx0+4fx1+2fx2+4fx3+…+4fxn-2+fxn-1, where Δ x = b-an,…

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.