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

Q: Evaluate the integral.

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

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

Q: Find the integral ∫dx / 1+coshx.

A: We write the function using ex

Q: Evaluate using integration by parts o a) (In 3x dx

A: As per the rules of the company we can only the first question and rest others can be reposted.

Q: Evaluate the trigonomnetric integral ∫(sint)5(cost)3dt

A: Given, ∫sint5cost3dt  We have to evaluate the  integral

Q: Calculate the integral. 2 / x + 4 dx

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Q: Find the integral

A: Given integral, ∫x16+8x2dx

Q: 1 dx X+4

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Q: Find the integral for f dx when n-4 by using Trapezoidal rule for five digits

A: Using  trapezoidal rule,Area=h2y0+y4+2y1+y2+y3Let fx=xx2+2, where, h=b-an=2-14=0.25          a=1,…

Q: Evaluate the integral ,(1 – x – 4x³ + 2x³) dx a) Analytically b) Single application of trapezoidal…

A: we have  f(x)=1-x-4x3+2x5 we need to find ∫-24f(x)dx  a) analytically b) using trapezoidal rule

Q: Evaluate the integral.

A: Recall

Q: Evaluate the integral ſ sin x dx by the method of geometry.

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Q: Find the integral. 3 dx

A: The given integration is indefinite integral of constant function.

Q: xarctanx dx

A: Product Rule of integration : ∫u.v dx = u∫vdx - ∫(dudx∫v dx)dx darc tanxdx = 11+x2 ∫ xn dx =…

Q: Using residues, calculate the improper integral 1 dx . 1+ x4

A: By using residue theorem the above integral is solved as follows

Q: Sec? ( 7x-8) dx =?

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Q: Evaluate the integral. arctan dx 1

A: For evaluating the given integral, we will use the concepts of integral by parts and integration…

Q: calculate the integral.

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

A: Given:Approximate the integral into four subintervals.

Q: Use the Trapezoidal Rule to evaluate the integral [x-'dx. .-1 1

A: Equation is f(x)=1xThe value of the table for x and y x 1 1.25 1.5 1.75 2 y 1 0.8 0.6667 0.5714…

Q: Find the integral. 4x dx

A: Let  I=∫4e4xdx Put    e4x=tTaking differential on both sides⇒e4x×4dx=dt        4e4xdx=dt Then, the…

Q: a) Use Trapezoidal and Simpson's Rule to evaluate the integral , (2x – 1)dx by taking n=4

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Q: Evaluate the integral. Vx + 25 dx Jo

A: Given that: ∫05x2+25dx

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

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Q: Find the approximation of the integral. 1= [e*dx Using Romberg's rule derived from Trapezoidal rule…

A: Given integral I=∫01e-x2dx Here we use Romberg's rule derived from Trapezoidal rule for 1,2,4,8…

Q: Use the midpoint rule with 4 rectangles to approximate (x? – a*) dx: The integral is approximately

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Q: Evaluate the integral.

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Q: Calculate the approximate to the integral -5 (24 +2x² − 3)dx, by the composite midpoint rule with…

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Q: dx = arcsec x + C xVx2 – 1

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Q: Evaluate the integral: + 6 dx = %3D

A: Find the integral by using substitution method

Q: Prove by using integration by change in variable the ff. integral: dx = arcsec x +C xVx² – 1

A: Our Aim is to prove the given integral given below by using change of integration.∫dxx(x2-1)dx -(i)

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

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Q: Зх-2 dx%3D V2x+3

A: We need to evaluate the following integral I = ∫3x-22x+3dx                            ........1

Q: dx -x - e

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Q: Evaluate the integral ∫dx / 1+sinx.

A: We need to evaluate the following integral: Rationalize the denominator, we get :

Q: 4. Use Trigonometric substitution method to evaluate the integral: dx

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Q: Evaluate the integral. dx 2x

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Q: Evaluate the integral. 3 (H) arctan dx /1

A: The given integral is

Q: sketch, reverse and evaluate the integral dy dx

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Q: Evaluate the integral. 8. dx 2

A: dxndx = n.xn-1 . ∫un du = un+1n+1+C

Q: -dx (4+5x)*

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Q: Evaluate the integral 4x³ dx

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Q: 1 dx

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Q: Approximate the integral | dx using 4 trapezoids .2 1

A: Introduction: The formula for the trapezoidal rule is given by, ∫aby(x)dx=h2y0+yn+2(y1+y2+...+yn-1)

Q: Use the Midpoint Rule with n = 4 to approximate the integral. %3D 14 x2 dx

A: We have to solve the integration using mid point rule.

Q: Use property 8 to estimate the value of the integral 1,12 15/0 - 58 a dx.

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Q: (a) In(4x) dx

A: Integration by parts:  ∫f(x)g′(x)dx = f(x)g(x) −∫f′(x)g(x)dx

Q: Evaluate the integral. * +5V dx

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Q: Evaluate the integral. 6 dx 2

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