The approximate value of dx by using Simpson's rule is 0.3480, then the error in the approximation is

Q: a) The shaded area is dx = |units? when rounded to five decimal places. Note: Apply five decimal…

A: We have to find area of the shaded region.

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: . 4x?y7 - x° +4y³ + 4) -2x=: 1. e* – sin(y) =x

A: During implicit differentiation, Differentiate both sides with respect to x and then seperate dy/dx…

Q: (a) 2-1 dx

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Q: The following problem is for extra practice and does not have to be submitted. 2 1 -dx using the…

A: According to question ∫0211+x3dx,       n=4

Q: Evaluate dy/dx at x = 2.5, correct to 3 significant figures, given y= (2x^2+3)/In 2x

A:

Q: 2. Use the composite trapezoidal rule with the step length h = 0.1 to evaluate dx I = 1+x2 and…

A: Composite trapezoidal and composite Simpsons 1/3rd rule

Q: Use Simpson's rule with interval h = 1 to determine the approximate value of 6 V(1 + x³)dx. Give…

A:

Q: Find the equation of the normal line to: y= (1+ cos ) e2 when x 0

A: The derivative of a function at a point is the slope of the function at that point. The product of…

Q: 5x2 dx et

A:

Q: Restate this question in terms of dV /dt and dh/dt: At what rate is water pouring in if the water…

A: Restate this question in terms of dV /dt and dh/dt: At what rate is water pouring in if the water…

Q: Find the indicated derivative and simplify. Int dy for y = dt et dt

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Q: Using appropriate substitution, the integral *+imx) dx is equal to: an

A: From the given problem:   I=∫141+lnx3xdx...1   Substitute in equation (1).   1+lnx=u...Differentiate…

Q: (a) Determine the interval width so that the composite trapezoidal rule can be used to compute xe*dx…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: to determine the approximate value of v(1+x³)dx

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Q: Find the most general antiderivative or indefinite integral. dx

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Q: Use Simpson's rule with interval h = 1 to determine the approximate value of f V(1+ x3)dx. Give…

A: Given integral is ∫021+x3dx and h=1. We have to approximate the given integral by using Simpson's…

Q: Without integrating, explain why: S, ?)°dx = o x(1+ x* -2

A: To show:     ∫-22x1+x22dx = 0 (without integrating)

Q: Find e dx approximately using Simpsons rule with n 10.

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Q: This is a calc 3 question    change the order of integration to dx dy dz

A: The given region of integration is bounded by all three axis and the plane:  x + y + z = 4.

Q: Make an octave code to integrate ex with respect to dx from 0 to 1, by Simpson’s ⅓ rule. Divide the…

A: Equation is f(x)=exThe value of the table for x and y x 0 0.25 0.5 0.75 1 y 1 1.284 1.6487…

Q: Use the Simpson's rule to estimate S, ex dx with n = 4

A: Consider the given integral ∫12ex2dx with n = 4. Simpson's rule is,…

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: Given tanh(x)+ tanh ¯' (y) = 1, show that, 1- y? 1 – x² dy dx

A: Formula,ddxtanh-1x=11-x2Note- Since multiple questions are asked, I am answering the first question…

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: ) Find MThe equation of The normal to 5 at the point (a, 4) y=dx

A: Given curve is x2+y2=5. To find the equation of normal at the point (2,1). Solution: Given curve is…

Q: 1+e* dx diverges 0.

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Q: Find the most general antiderivative , verify answer by differentiation  g(x)=7sin theta/3

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Q: Use x = e to explain why dx (In x) = = -, for x> 0.

A: To differentiate x=ey, with respect to x, use the exponential function rule, ddxef(x)=ef(x)ddxf(x).…

Q: Use the Trapezoidal Rule with n = 6 to ex approximate dx | 1 х Use the Simpson's Rule with n = 6 to…

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Q: 1 Evaluate dx by using Trapezoidal rule. Hence obtain 1 + x2 he approximate value of .

A: I am attaching image so that you understand each and every step.

Q: To evaluate S (In x)² -dx, apply integration by parts twice. For the second application of…

A: Follow the procedure given below.

Q: dx is: value of the integral sinx the Using Simpson's rule 113,

A:

Q: Solve the following Exact DE using Method of Grouping. 3) () dx + () dy = 0 X-X y

A: Given:          2x-1ydx+x-x2y2dy=0     This is in the form of   Mx,ydx+Nx,ydy=0    where Mx,y=2x-1y…

Q: Using the trapezoidal rule with n = 5, approximate the integral L' TO S³ give the error of…

A: Trapezoidal rule formula: ∫abf(x) dx=h2(y0+yn)+2(y1+y2+...+yn-1) Given ∫03dx16+x2 Here f(x)=116+x2…

Q: Use Simpson's rule with interval h = 1 to determine the approximate value of V(1 + x³ )dx. Give…

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Q: –1 dx

A: Solve the following

Q: Use the composite trapezoidal and Simpson's rules with step length h = 0.4 to estimate In(2+3/x)…

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Q: |2²+2x + 1 dx

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Q: Calculate an approximate value of the integral x2 dx by dividing the 1+x interval into 4 equal parts…

A: In the question we have to find the value of integral by using Simpson's one - third rule.

Q: Use the Simpson's rule to estimate e**dx with n = 4

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Q: 7) Estimate the value of e dx using Simpson's rule using 8 subintervals.

A: Given: ∫02ex2dx Here, n = 8 subintervals

Q: Find / tan- -dx using integration bv parts. TM

A:

Q: Approximate S“ In x dx using three rectangles of equal length and left end points. Is your estimate…

A: The given integral ∫1e2ln x dx, three rectangles and left end points.

Q: Determine the mean and the rms values of the following by direct integration method a. f(t) = sint…

A:

Q: Use the Trapezoidal Rule with n = 4 to approximate the value of: +1)dx.

A: Given,  ∫12x3+1dx, n=4

Q: Use the Trapezoidal Rule with n = 4 to estimate f, x² dx. Compare the estimate with the exact value.

A:

Q: Let y = sin(5x). If Aæ 0.4 at x = 0, use linear approximation to estimate Ay %3D Ay = %3D Find the…

A: delta y here represents the change in the value of y when x changes from x= 0 to x =0.4.

Q: The approximate value of| dx by using Simpson's rule is 0.3639, then the error in the approximation…

A: Approximate value of ∫161x4dx by using Simpson's rule is 0.3639 To find the error in the…

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.