2. Use the composite trapezoidal rule to estimate the integral of y = sin(x) %3| from x = 0 to 2. Use the number of steps, n=4. Also, calculate the true error of the estimation.

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: (b) Find a value for n to ensure that the absolute error in approximating the integral xsin x dx by…

A:

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral S7 n = 20…

A: we nee to find ∫π4π2ln(tanx)dx,  n=20 a=π4=0.7854,  b=π2=1.5708 ,  y=ln(tanx)…

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

A:

Q: How large should we take in order to guarantee that the Trapezoidaland Midpoint Rule approximations…

A: Given

Q: Evaluate the double integral ∫0 to 1 ∫√y to 1 SQRT(2 + x^3) dxdy by reversing the order of…

A:

Q: The error is numerically computing the integral | 1 dx using the +4 trapezoidal rule with two…

A:

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

A:

Q: Evaluate the integral by using a substitution prior to integration by parts. 9 sin ( In (8x)) dx 9…

A: To integrate

Q: By using trapezoidal rule, n=2, The integral = π/2 sin (x) dx 0.9444 O 0.9481 O 0.94809 O 0.9482 O…

A:

Q: Find a value for n to ensure that the absolute error in approximating the integral x cos x dx by the…

A:

Q: The approximated value of the integral fe* dx is equal to - Rule with step size (h=2). when using…

A:

Q: (a) Use the Midpoint Rule with n = 6 to approximate integral S³ dx 8 x-6 6 x+8

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: Evaluate the improper integral |. 3.x dx or show that it diverges. +1 x?

A:

Q: 34. x sec xdx

A:

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

A: We need to use the mid-point rule to find the value of the definite integral.  The mid-point rule…

Q: Approximate the integral from pi to 0 of 5sinx dx using four equal subintervals.

A: Given:Approximate the integral into four subintervals.

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: dx x²+18

A: Given, I= ∫x²/√(x²+18) dx

Q: (a) Use the Midpoint Rule with n = 6 to approximate integral 8 x-6 S8 dx 6 x+8 ?

A: As per the instruction, we will be answering the first question. Given:

Q: Evaluate the integrals using integration by parts. ∫sin-1 y dy

A: Evaluate: ∫sin-1ydy

Q: Use the Trapezoidal Rule to approximate the integral of e^(3/x) dx from 2 to 3 with n=4 . Round the…

A:

Q: Approximate the integral from 1 to -3 of e-x dx using four equal subintervals.

A:

Q: Evaluate the integrals using the substitution method of e8x dx

A: To evaluate the integral: ∫e8xdx Solution: Let substitute t=8x. Differentiating both sides, we get…

Q: Show using residues that   the integral from 0 to infinity of dx/(1+x^6) equals (2pi)/3

A: We have to show that ∫0∞dx1+x6=2π3 by using residue theorem. Now, ∫Cdz1+z6=∫−RRdx1+x6+∫γdz1+z6 Now,…

Q: Use integration by parts to find the integral. xeax dx (a # 0)

A:

Q: How large should n be to guarantee that the Simpson's Rule approximation to the integral from 0 to 1…

A: How large should be n such that, by using Simpson's (1/3) rule we have  ∫013ex2dx=0.0001.

Q: 5 sin (x) cos(x) In(sin(x)) dx

A:

Q: Use Simpson's Rule with n = 4 steps to estimate the integral. 42) | 7 dx 1+X

A:

Q: Use Simpson's Rule with n = 4 steps to estimate the integral. dx O 18 O 15 36

A: Given:    f(x) = x  Limit: 0 to 6    n = 4

Q: Use Simpson rule' 1/3 Method with (n = 8) to estimate the integral: f(x) : e^(sin 9x), where a = 0 &…

A: Given; f(x) = e^(sin 9x) and n=8 And a=0 , b=10

Q: Using the trapezoidal rule with n = 4, estimate the integral / (x (x+1)² dx.

A:

Q: Estimate the integral below by using Simpson's rule and Trapezoidal method with n=4, also find ET…

A:

Q: Evaluate the integrals ∫sin7 y dy

A: ∫sin7y dy On simplification, we get ∫sin7y dy=∫sin6y·siny dy=∫sin2y3·siny dy=∫1-cos2y3·siny dy…

Q: Find the improper integral. (If the quantity diverges, enter DIVERGES.) dx (x² + 16)3/2

A:

Q: For Trig integration find the integral of  Sec^6(6x)

A:

Q: 2. Use the error formula to estimate the error in approximating the integral T/2 2 sin x dx using…

A:

Q: Use (a) the Trapezoidal Rule integral 1to 4    sin x dx                 with n= 5

A:

Q: Evaluate the following integrals using integration by parts method: x sin 2x dx

A:

Q: Estimate the minimum number of subintervals needed to approximate the integrals with an error of…

A: Here I have appended the formula used in the solution part

Q: Find the integral by using the appropriate formula. (Use C for the constant of integration.) In x dx

A:

Q: Find the minimum value of n that guarantees an error of no more than 1/30,000 in approximating the…

A: Given the integral: Hence we have

Q: Evaluate the integral by using a substitution prior to integration by parts. 9 sin ( In (4x)) dx 9…

A: The given integral is 9 sin[ln(4x)]

Q: 2. Estimate the integral using Simpson's approximation rule with n=4: sin t dt

A: To estimate:∫0πsint dtn=4

Q: By finding an antiderivative, evaluate the integral, where the contour is any path between the…

A:

Q: 1.a) Apply the Trapezoid and Corrected Trapezoid Rule, with h =, to approximate the integrale-2x²…

A: (a). Given integral is ∫13e-2x2dx. The step size is h=18. We know that the integral of a function fx…

Q: Use any method to evaluate the integral. x'dx 2 X + 16

A:

Q: 3.a) Apply the Trapezoid and corrected trapezoid rule, with h =, to approximate the integral…

A:

Q: 4. Evaluate this integral by reversing the order of integration: Vy3 +1 dy dx.

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.