Prove that integration of (x/sigma square ) times exponential of (-x square/2sigma square) for limit 0 to ♾ is 1

Q: Evaluate the integral if it converges and enter the exact value. If the integral diverges, indicate…

A: The given integral is ∫-1216x-13dx. We also know that ∫xndx=xn+1n+1.

Q: (x² + 1)cos x x4 -x + 2

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Q: Evaluate the following and use change of bounds for definite integrals when appropriate.

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Q: Determine whether Ln=1 n2+1 tan- is convergent using integral test.

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Q: n, ]x| fn (x) = - 2m 0, x > 2n | fn (x) cos x dx lim Calculate its limit. What happens if the limit…

A: Write the integral as limn→∞∫-11fnxcosx dx=limn→∞∫-1-12nfnxcosx dx+∫-12n12nfnxcosx dx+∫12n1fnxcosx…

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

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Q: 4. 5⁰ -x² xe dx

A: Given Problem:- ∫0∞xe-x2dx

Q: Find the lower bound of sum 2-1 using an integral

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Q: Use Simpson rule’ 1/3 Method with (n = 6) to estimate the integral f(x) = x / ((9*x^3)-3), where a=…

A: Fghhhj

Q: 4. Determine if the Mean Value Theorem for Integrals applies to the function f(x) = x³ - 9x on the…

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Q: Express the limit as a definite integral on the given interval. lim n → ∞  n [2 − 5(xi*)2 + 6(xi*)4]…

A: Given query is to find the integral form of limit.

Q: Determine the first two nonzero terms in the expansion about zero for the function f(x) = [tan(x) -…

A: According to the given information the given function is:

Q: 2) Use Newton's method to approximate the zero in f(x) = - x3 + 3x-x + 1, or explain why Newton's…

A: Consider the given function,

Q: Suppose that f is an integrable function on R (real numbers).  How do you show that the integral  of…

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Q: Evaluate the definite integral: 6/x with the upper limit being 5 and lower limit 1

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Q: Use Simpson rule’ 1/3 Method with (n = 8) to estimate the integral: f(x) = 5x*((13x - x²)³)½ , where…

A: To evaluate the definite integral by the Simpson's 13 rule, use the following formula.…

Q: Evaluate the definite integral: x²)dx using limit of the Riemann sum.

A: Consider the provided definite integral, ∫02 2-x2dx Evaluate the provided integration using limit of…

Q: Find the values of p for which the Integral converges. (Enter your answer as an inequality. 25…

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Q: Find the number of subintervals that will ensure that the absolute error in approximating the…

A: Using Simpson 1/3 rule.

Q: Evaluate the indefinite integral as an infinite series. 1- COs x dx | 13. x2

A: We have to evaluate the integral as an infinite series.

Q: 1) In order to use the integral test, we must verify that the sequence is decreasing (and positive…

A: We have to test series is convergent or divergent

Q: The integral of ƒ In(ln(x))dx can not be expressed as a finite sum of functions. What do we call…

A: It is called as non elementary integral

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

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Q: Express the limit as a definite integral on the given interval. lim n - 00 -Дх, [1,5] (x*)2 + 6 dx

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Q: What is the interval of convergence of Taylor Polynomial of f(x)=cos x at a=pi/3

A: Given function: fx=cosx a=π3 The Taylor polynomial of the function f(x) at x=a is given by…

Q: Determine whether the integral is convergent or divergent. x arctan(x) 11 dx (1 + x2)2 convergent…

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Q: Use the intermediate value theorem to show that there is a solution to x− √ x−ln x = 0 on the…

A: Use the intermediate value theorem to show that there is a solution to x− √ x−ln x = 0 on the…

Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it…

A: Given integral is ∫0∞e-1xx2dx. We know that integral converges if it has a finite value. Evaluating…

Q: Express the limit as a definite integral on the given interval. -Дх, [1,4] (x;)2 + 9 lim i = 1 dx

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Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it…

A: Here given integration as I=∫2∞1xx2-4 Since ∫1xx2-a2=1asec-1xa+C

Q: solve the integral: I2=  integral limit from 0 to 4= 1/((x+1) squar root of 2x+1) dx

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Q: -x² xe* dx -00

A: Given: ∫-∞∞xe-x2dx

Q: Use the definition of definite integral (as the limit of a sum) to evaluate | (2x – 1)° dzr.

A: ∫-212x-12 dx Here, a=-2,  b=1  &  fx=2x-12 Now, ∆x=b-an=1--2n=3n

Q: calculate the limit of ln(x) - (e)^x  x goes to + infinite

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Q: 1. Use the definition of the definite integral as the limit of a sum to evaluate (4.x – 2²) dx.

A: The given problem can be solved as-

Q: Estimate the area under the graph of the function f(x)=1/(x+5) from x=0 to x=4 using a Riemann sum…

A: To estimate: The area under the graph of the function f(x)=1/(x+5) from x=0 to x=4 using a Riemann…

Q: Determine whether the integral is convergent or divergent. x arctan(x) 00 11 dx (1 + x2)2 convergent…

A: Given integral, I=∫0∞11xtan-1x1+x22dx Used formulas, ddxtan-1x=11+x2ddxx=1…

Q: Express the limit as a definite integral on the given interval. * n Χρισ lim Σ -ΔΧ, [1, 8] 0-00…

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Q: Estimate the area under the graph of the function f(x)=1/(x+5) from x=0 to x=4 using a Riemann sum…

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Q: Evaluate the definite integral: (2 – a²)dx using limit of the Riemann sum.

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

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Q: Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation…

A: Let's find.

Q: Let -(x) be the Taylor polynomial of degree for the function x) = cos(x) at = 0. Suppose you…

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Q: The approximate value of a definite integral that is obtained using the simpson's rule will always…

A: We have to find the given statement is true or false. Let us consider the example given below

Q: 2. Determine if the integral converges or diverges. Part of your grade on this problem depends on…

A: Topic:- integration

Q: 1. Write the Riemann sum for the function (x) = x + x² by dividing [0,2] into n equal subintervals…

A: Dividing the given interval, [0,2], into n equal sub-intervals, the width of each interval will be:…

Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it…

A: Integration:       ∫3∞ 1xx2-9dxLet us keep the substitution,…

Q: Determine whether the integral is convergent or divergent. x arctan(x) 75 dx (1 + x²)2 O convergent…

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Q: Use integration by parts to evaluate the definite integral: ∫3se^-4s ds with an upper limit of -0.9…

A: A=3∫abse-4sds , solving A where a,b are upper and lower limits as per questionIntegrate by parts…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.