Estimate the minimum number of subintervals needed to approximate the integral dx with an error of magnitude less than 10-4 using Simpson's Rule.

Q: Use the Trapezoidal Rule and Simpson's Rule with four subintervals to estimate x* dx.

A: Trapezoidal Rule

Q: Set up a definite integral for the length of the curve y = x3 over [1, 2]. Set up the integral and…

A:

Q: Use integration by parts to compute the integral S xsin(4x)dx and Inx dx

A:

Q: use interval additivity to show that  (integral a to b)(x+1)^2 dx = F(b) - F(a)

A: Solving by interval addditive property we have

Q: Approximate the area under the curve y=x3 from x=0 to x=2 using a Right Endpoint approximation with…

A:

Q: 1. ntegral dx with 6 (x-4)2

A:

Q: Approximate the area under the curve Y=x3 from X=1 to X=4 using a Right Endpoint approximation with…

A: To find out the area under the curve using the right endpoint approximation with n=6

Q: Find the area under the curve y= 1/(4x+ 2) for 1 ≤ x ≤ 3. Give an exact answer.

A:

Q: Use Simpson’s Rule with n=4 to approximate the integral 8∫0√xdx.

A:

Q: Approximate the area under the curve y = x° from x = 3 to x = 5 using a Right Endpoint approximation…

A:

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.