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: The surface area of a sphere, initially zero, increases uniformly at the rate of 4 xq.in. per sec…

A:

Q: (a) Use the trapezoidal rule to approximate the integral. dx

A: Solution of given question is written in below steps.

Q: Use a CAS double-integral evaluator to estimate the values of theintegrals

A: Consider the given integral ∫01∫01 tan-1xy dy dx

Q: 3 Estimate the integral 1 dx by the trapezoidal rule using n = 4. + 1 Vx3

A: ∫abf(x)dx≈Δx(f(x0)+f(x1)2+f(x1)+f(x2)2+f(x2)+f(x3)2+⋯+ f(xn−1)+f(xn)2) where ∆x =b -an

Q: Use Simpson's Rule with n=2 subintervals, evaluate the integral - Inx. dx, and compare the estimate…

A: Here we use Simpson's rule with n= 2, evaluate the integral value and compare the estimate with…

Q: The value of the integral Vx dx computed using Trapezoidal rule with 2 subintervals is (Rounded upto…

A: The trapezoidal rule uses the area of the trapezoids to approximate an integral. Using the…

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

A: Given

Q: evaluate the incdesinite integral -5x+3)dx

A: See the details solution below

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

A:

Q: Calculate an approximate value of the integral ; dx by dividing the 1+x2 interval into 8 equal parts…

A:

Q: Evaluate the integral by reversing the order of integration. 6ely dy dx

A:

Q: With the help of simple fraction s separation method dx Caleulate the integral.

A:

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

A:

Q: 1- Estimate the minimum number of subintervals needed to approximate the integral with an error of…

A: Solution-

Q: Find the approximate value of integral from 0 to 10 1/√(x2+1)dx to 4 decimal places using Simpsons…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 7 arctan(x) dx

A:

Q: Use Simpson’s rule with n = 4 to approximate the value of integral.

A: Consider the given integral as ∫01exex+4dx

Q: –1 dx x V In (-x) -3

A: Find the type of the generalized integral and examine its convergence.…

Q: Evaluate the integrals by using a substitution priorto integration by parts. ∫ln (x + x2) dx

A:

Q: Evaluate the integral by reversing the order of integration. dx dy

A:

Q: Use the 4_segment trapezoidal Rule to numerically integrate. S(0.2 + 25x + 3x²) dx

A:

Q: 18) Use two compositions of composite Simpson's method to estimate the integral S" Inx dx

A:

Q: Use Simpson's Rule with n = 4 to estimate the following definite integral: %3D a +32 dx x + 2

A:

Q: use the trapeziodal and semson rule to approximate the following integrals

A:

Q: Evaluate the integral. (Use C for the constant of integration.) (arctan(x))5 | x2 + 1 dx

A:

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

A:

Q: Evaluate the following integration: 3x-2)dx Using trapezoidal rule for 100 and 1000 equal segments.

A: Given integration is ∫02x5+3x3-2dx Solution a: let f(x)=x5+3x3-2 Using Trapezoidal rule Here equal…

Q: Evaluate the integrals by using a substitution priorto integration by parts. ∫x tan2 x dx

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Given (3x + 5x') dx, use Simpson's rule with 4 subintervals to determine an upper bound for the…

A:

Q: Use the Midpoint Rule to approximate the integral 13 | (- 2x + 10æ²) dx with n=3.

A:

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

A:

Q: Find the approximate value of the integral using Simpson's Rule. (a) So" vsin x using n= 6…

A:

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

A:

Q: Approximate the integral dx using Simpson's Rule and four rectangles.

A: Given,  ∫121xdx

Q: Evaluate the integrals by using a substitution priorto integration by parts. ∫sin (ln x) dx

A: Given: I=∫sinlnxdx for evaluating given integral, we substitute lnx=t…

Q: 3. Approximate the integral -dx using 4 trapezoids.

A:

Q: 2. Use the composite trapezoidal rule to estimate the integral of y = sin(x) %3| from x = 0 to 2.…

A:

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

A:

Q: The Simpson's nule of numerical integration applies, if number of subintervals (n) is a multiple of

A:

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

A: To estimate:∫0πsint dtn=4

Q: Evaluate the integral by using u-substitution and changing the limits of integration. x3 dx -1 ex*+1

A:

Q: Find the average value of the function on the giveninterval.   f(x)   = Sin4x  , [-π ,π]

A: Given- fx=sin4x To find-  The average value of the function on the interval -π,π. Concept Used- The…

Q: Use the trapezoidal rule with n=6 subintervals to approximate the integral 1 to 4  ln(x+sqrt(x)) dx.

A:

Q: State the Comparison Theorem for Improper Integrals. As well, use it to determine whether x + 2 dx…

A: For the solution follow the next step.

Q: ) dx

A:

Q: Use the Trapezoidal Rule withn=4 steps to estimate the integral. 3 16) dx Use Simpson's Rule with n…

A: 1.  According to the Trapezoid rule,…

Q: Using tabular integration, the integral In 2 S™ (-2x + 1)e²x dx is equal to

A:

Q: Use Simpson's Rule with n = 4 steps to estimate the integral. 5) dx

A:

Q: Calculate the improper integral if it converges, or show that it diverges. 1 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.