By applying the convolution theorem to calculate L-1(14/[(s + 4)² + 25] ), an adecuate integral for the calculus would be: photo 3

Q: f sec¹ x dx

A: Integrate the integral sec7x .

Q: Solve the integral by trigonometric substitution: (z+3)* dz. (40 – 6z – 22) - -

A: Given: To solve the given integral by trigonometric solution: ∫(z+3)540-6z-z232dz

Q: Express the limit as a definite integral on the given interval. -дх, [1, 6] (x;)2 + 8 lim n- 00 i =…

A: Given limn→∞∑i=1nx*ix*i2+8Δx and 1,6 We have to express the given limit as a definite integral.…

Q: x arcsin(x²) dx;

A: Given that: *∫sin-1u×du=u×sin-1u+1-u2+C The given expression is, ∫x×sin-1x2×dx Let,  x2=u,…

Q: Consider the segment of the parabola ƒ1x2= x2 on the interval 30, 24. a. Write the integral for the…

A:

Q: Calculate  lim as n approaches infinity of the integral from 0 to 1 of (ncosx)/(n+ex) dx. Justify…

A:

Q: The smallest positive, nonzero root of cosh x cos x - 1 = 0 lies in the interval (4, 5). Compute…

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Q: Find the exact value of the integral using formulas from geometry. 5 (3+ 2x)dx 1

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Q: Use Cauchy's Integral Formula and Cauchy's Integral Formula for Derivatives, when appropriate, to…

A: Given integral: ∮Ce5izz4-z4z-i3dz closed curve is z=4. Cauchy integral formula: fw=12πi∮Cfzz-wdz…

Q: Evaluate the definite integral by the limit definition

A: Here,

Q: Find "(x2 + 3)dx using the definition of definite integral (i.e. using a limit of Riemann sums).

A: Solve the following integral

Q: 3. Determine the number of sub-intervals required to approximate 3 -x² dx e using the Trapezoid Rule…

A:

Q: 2 How many subintervals does the composite trapezoid rule need to obtain the approximation of the…

A: Given function is

Q: Use the Midpoint Rule with n = 3 to approximate the integral 4 | (7x – 52)dz 52²)dr

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Use the methods of (1) left Riemann sum, (2) right Riemann sum, (3) trapezoidal rule, (4) parabolic…

A: According to our company's guidelines I can only answer first three subparts of the question since…

Q: (1,2) (b) Set up a definite integral that is equal to the arc length of the portion of the circle…

A: Note:- As per your request i am solving here question no. 3 part B only.

Q: With the equation y = lnx+1 on the interval 1 ≤ x ≤ 2, please set up but do not evaluate the…

A: for rotation about x axis :

Q: Use the methods of (1) left Riemann sum, (2) right Riemann sum, (3) trapezoidal rule, (4) parabolic…

A: Since you have sent multiple parts therefore we can solve just 3 sub-parts according to our…

Q: Use substitution to find the indefinite integral. 2. zy5z 5z²-8 dz 2. - 8 dz =|

A: The given integral is: I=∫z5z2-8 dz

Q: Use the definition of the definite integral to evaluate fo (2x – 1)dx. Use a right-endpoint…

A: To Find: a. Use the definition of definite integral to find ∫032x-1dx.b. Use right-endpoint…

Q: Use substitution to find the indefinite integral. 2 | 5z² – 3 dz -3 dz =

A: Given: I=∫z5z2-3dz   ...1   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: If a force of 128 lbs is required to stretch a 10-ft spring by 4 ft. How much work is done by…

A: Here we have to use the concept of integral calculus

Q: How do I use Riemann's sums?

A:

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

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Q: 20. V9 – x² dx

A:

Q: Use integration by parts to obtain the formula dr. sarating Invorc of Funotiono

A: Given:∫1-x2 dxIntegration formula:∫sinx=-cosx+C∫xn dx=xn+1n+1

Q: 3. Express the given integral as the limit of a Riemann sum but do not evaluate: So (x³ - 6x) dx.

A: Solution:-

Q: 4, by 2- Approximate each of the integrals in the following problems with n (i) The trapezoidal rule…

A: Trapezoidal rule: The area under the curve y = f(x) over the integral [a, b], when it divided into n…

Q: Express the limit as a definite integral on the given interval. lim n- 00 [4(x;)³ – 4x;"]ax, [(2, 7]…

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Q: sin x dx < 12 12 T/6 VI

A: Given π12≤∫π6π3sinx dx≤3π12 Here fx=sinx

Q: Use the definition of the definite integral to evaluate approximation to generate the Riemann sum. 3…

A:

Q: xp

A: According to Residue Theorem if z=z1, z2, z3 ..., zn are the singularity of f(z) then∫c f(z)  dz = 2…

Q: A hole of radius 3 is bored through the center of a sphere of radius 5. Let the cross- section of…

A: we will draw region which can be rotated to create solid region whise volume needed to find . Then…

Q: Use the definition of the definite integral to evaluate ∫02 (3x2 +1)dx. Use a right-endpoint…

A: As a first step, let's plot the graph of the curve given to us. Let's call the curve y = f(x) = (3x2…

Q: only the limits of the integration

A: We have to find out the limit of the given integration. The given integration is I=∫∫Rdxdy

Q: Give the Riemann sum approximation for the definite integral S° dx using n = 4 subintervals and left…

A: Left reimann sum

Q: Express the limit as a definite integral on the given interval. exi Ax 3 + x; lim [0, 4] dx

A: We need convert summation in to integral

Q: linear density of a rod of length 16 m is given by p(x)=25square root x+4 measured in kilograms per…

A: Explanation and solutions is given below....

Q: 28. X (1+4x²)³ dx

A:

Q: Express the limit as a definite integral on the given interval. n exi lim -Ax [0, 9] n→∞ i = 1 6 +…

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Q: Evaluate the integrals using trigonometric substitution dz 2² √2²-4

A: Find the inegrals by Trignormeric substitution

Q: Express the limit as a definite integral on the given interval. cos Xi lim Ax, [3π, 5π] 818 5m 3m dx

A:

Q: Evaluate the integral using Trigonometric Sub 3 + 2z + 11)ždz 2

A:

Q: Use the definition of the definite integral as a limit of a sum to evaluate (x² – 4x - 2) dx -2

A:

Q: Express the limit as a definite integral on the given interval. lim 2 x;)?+9 -ах, [1,4] (x;")² + 9'…

A: Use;∫abf(x) dx =limn→∞ ∑n=1n f(xi) ∆x                       over the given interval [a, b].

Q: Determine the integral by algebraic substi tution first then by trigonometric substitution: * 3z dz.…

A: ∫3z1-4z-2z22dz   ∫3z1-4z-2z22dz=3∫z+1-11-4z-2z22dz ∫3z1-4z-2z22dz=3∫z+11-4z-2z22dz-3∫11-4z-2z22dz…

Q: Solve the integral by two grid in the y-direction and four grid in the x-direction with Trapezoidal…

A: The given integral is: ∫45∫23xcosydydx Here  x0=4, x1=5y0=2, y1=3fx,y=xcosy By Trapezoidal rule,…

Q: Find Lebesque integral of function on segment (0,1) f(x) = if- 7h+1

A: In the given question we have to find the Lebesque integral of the given function…

Q: -dz 22 + 4z Use Cauchy's theorem or Cauchy's formula to compute integrals and -dz. 22 + 4 Reme mber…

A: Given that ∫z=1ezz2+4zdz and ∫z=1ezz2+4dz. Thee objective is to find the integral values using the…