Use Simpson's rule to evaluate 1 -dx, by dividing the interval into 4 equal (5x-2) parts. Find the error comparing with the exact value.

Q: Find the integral. er sin(5x)dx - IT

A: Known integral formula:

Q: fx sin(5x)dx

A: use integration by parts take

Q: (d) Calculate the value of dx correct to 3 significant figures taking six intervals by Trapezoidal…

A:

Q: Estimate | (2x – 5) dx using left endpoints for n = 3 approximating rectangles. %3D 5 (2x – 5) dx is…

A: Given: ∫152x-5ddx The left Riemann sum (also known as the left endpoint approximation) uses the left…

Q: Use integration tables to find or evaluate the integral.

A: The question is taken from the calculus in which we have to find the integral of given question We…

Q: sinxcos 2x dx

A:

Q: Estimate sinx? dx with an error of less than 0.001.

A: Given ∫01sin(x2)dx

Q: Use the midpoint rule with four subdivisions to estimate ∫2 to 6 (2x2+3)dx to two decimal places.…

A: Given ∫262x2+3dx we have to use midpoint rule

Q: Calculate the deriv L tan2tdt d_ dx II

A: Derivation of          is calculated as shown below

Q: 4 x ) dx. 4 tan x

A: topic - definite integral using integration properties

Q: Use the Midpoint Rule with n = 4 to estimate (x² + 1) dx %3D

A: Given:        ∫02x2+1dx       n=4 , a=0, b=2   Midpoint Rule…

Q: In integrating the function fxIn Sx dr using integration by parts, what would be your du? du = In 5x…

A:

Q: Use the tabular method to find the indefinite integra. ∫x2(x − 2)32 dx

A:

Q: sin(3 dx

A:

Q: How do you use a Maclaurin serieis aproximation to estimate (Provided picture). Thanks!

A: First find the Maclaurin series for e^(x^2) using the Maclaurin series of e^xPlug x^2 in place of x.

Q: Select the correct answer. What is the value obtained by using left endpoints with n= 4 subintervals…

A:

Q: By using Trapezoidal rule, the value of "h" in evaluating [(r' - 2x + 6)dx , by taking 10…

A:

Q: By dividing the range into 8 equal parts, evaluate dx using Simpson's rule.

A:

Q: Use the midpoint rule to calculate the absolute error of (4x² + 1) dx using 3 subintervals. Enter an…

A: Given query is to find the absolute error of Integral.

Q: Use Integration by Parts, with u = x and dv = sin(3x + 4) dx.

A: u = x and dv = sin(3x + 4) dx.

Q: 2 By using Trapezoidal rule, the value of "h" in evaluating - 2x + 6)dx , by taking 10 subintervals…

A: Solved below

Q: Use integration by parts to evaluate the integral sin(10x)/e^2x dx

A:

Q: Use Simpson's rule with 3 8 intervals, to evaluate 2 dx, correct to 3 decimal places.

A:

Q: Use the trapezoidal rule with n = 2 to approximate the value of sin(x²)dx. Round your answer to four…

A:

Q: Use integration by parts to prove the reductionformula.

A: We have to prove the reduction formula using integration by parts method: ∫xnexdx=xnex-n∫xn-1exdx If…

Q: What is the area of the region between the sine curve and the x-axis from to 2 ? -1 2 1 4 3.

A: Here we have to find the area of the region bounded by the sine curve and the x-axis from π2 to 2π.…

Q: rea of the region between the sine curve

A: Here we have to find the area of the region bounded by the sine curve and the x-axis from π2 to 2π.…

Q: S sin³x dx

A: Let's recall the formula underlying integration by parts:

Q: By using Trapezoidal rule, the value of “h" in evaluating (x² – 2x + 6)dx , by taking 10…

A:

Q: Use Simpson's rule to evaluate [ 1 -dx, by dividing the interval into 4 equal (4х- 3)° parts. Find…

A: In the question it is asked to solve the integral using Simpson's rule.

Q: (3X dx =? Sinmply

A:

Q: Which integral requires more steps to find? Explain. Do not integrate. | sin° x dx OR sin°x cos x dx

A:

Q: 4x dx.

A: Given I=∫02e-4xdx Here fx=e-4x,a=0,b=2,n=4 . Then h=b-an=12 Therefore, the subintervals are…

Q: Integrate x sqrt of (x+4) dx using algebraic substitution

A:

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

A:

Q: Use integration by parts to evaluate the integral: sin(x)dx

A:

Q: Approximate sinx dx using four trapezoids of equal width. On the interval (0, pi)

A: Trapezoidal rule

Q: Evaluate Sx In(sinx)dx

A:

Q: Estimate 4 - x dx using midpoints for n= 4 approximating rectangles. 2 4 – x dx is approximately

A:

Q: use integration by parts to write the integral sec^7 (3x) dx in terms of integral sec^5 (3x) dx

A: ∫sec7(3x)dxPut 3x=uso 3dx=du=13∫sec7uduNow ∫sec7udu=∫sec5usec2udu

Q: V9x² – 5 - dx . .2 fact to determine the integral 9x?

A:

Q: To approximate cos(x) dx would Simpson's Rule, Midpoint Rule, or Trapezoidal Rule give a better…

A: The exact value of the given integral is 1

Q: Evaluate π' sin(πα) da

A:

Q: Evaluate the integral:∫sin3x dx.

A: The given integral is ∫sin3x dx

Q: Use integration by parts to evaluate (tan- dx. Express your answer in four (4) 2 decimal places.

A: By part integration: integration uv = u(integration v) - integration ( (u')(integration v))

Q: Find integral 2  to 5    1/ sqrt  (x -2 ) dx

A:

Q: Compare the Trapezoidal rule and Simpson's rule approximations to x sin x dx and find a bound for…

A:

Q: How large should we take n in order to guarantee that the Trapezoidal Rule approximation for 6 5x*dx…

A:

Q: Use integration by substitution or integration by parts as appropriate to evaluate Axsin (Bx) dx…

A: We are given A=3 and B=3 now putting the values in integral it becomes ∫0π23xsin(3x) dx first we…

Q: Use Trapezoidal method to evaluate (2x/2-x dx, by dividing the interval into 4 1 equal parts. Find…

A: According to question given that∫122x2-x2dxn=4

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.