Consider the function: fx = 1/(4sqrt(2pi))*e^(-1/2*((x-3)/4)^2) Determine its value: a) integral from -infinity to infinity of fx dx

Q: Use the Comparison Theorem to determine whether the integral is convergent or divergent. sec2(x) 4…

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Q: Express the limit as a definite integral on the given interval. cos(x¡) Дх, [Зл, бл] Xi lim бл dx…

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Q: Evaluate the integral. (Use C for the constant of integration.) / test at

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A: The solution is given below

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A: Hint : 1. Use substitution : ex = t. This integral will turn into a standard Integral.

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Q: Express the limit as a definite integral on the given interval. n lim x, In(2 + x,-) Ax, [0, 4] i =…

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Q: . Find the area of region between two functions fix)=sinx, g(x)-cos2x,-끌sxs을 %3D

A: The area between two curves A=∫abf(x)-gxdx sinx=cos2xsinx=1-2sin2x2sin2x+sinx-1=0sinx=-1±1+84=-1,…

Q: xlnx at 0<x<1 1-X Show that the function f(x)= is integrable on the interval [0,1]. x = 0 x = 1 at…

A: Given: fx=xlnx1-x,0&lt;x&lt;10,x=0-1,x=1 To prove: f is integrable on 0,1.

Q: Evaluate the definite integral by the limit definition

A: Here,

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A: Given :

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Q: Evaluate a. Fв- x-3Dаx

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Q: Use Simpson's Rule and n = 4 to find an approximation for the definite integral Vr +1 dr %3!

A: Here, the given function is: f(x)=x3+1 Now, the Simpson's rule formula to approximate the definite…

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A: In this question, we find the line integral for given vector function and parametric path.

Q: Express the limit as a definite integral on the given interval. [5(x;)3 - 3x;]Ax, [2, 6] n- 00 i = 1…

A: see below the answer

Q: Sketch the graph the integrands and use areas to evaluate the integrals. V16 – x² dx

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Q: Evaluate the definite integral by the limit definition.

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Q: What is meant by indeterminate integral

A: Definition: An improper integral is the limit of a definite integral as an endpoint of the…

Q: Use integral tables to evaluate. 1 dx; x> 3. 2xV9x -1

A: The following integral: ∫32x9x2-1dx; x&gt;13.

Q: Eind to approximation to Jas corect decimal an three places

A: The given expression is 253. Let y=x13, where x=27,∆x=-2 as 25=27-2. That is, y=2713=3 Obtain ∆y:…

Q: Use the definition of the definite integral as a limit of a sum to evaluate 1 (x² – 4x – 2) dx -2

A: Given the integration of (x^2 - 4x -2) from limit  -2  to 1.

Q: Use the mid-ordinate rule with four intervals to evaluate the integral Type your final answer below…

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Q: Evaluate the definite integral by the limit definition. 3x2 dx

A: Please refer the attached image for complete solution. THANK YOU.

Q: Express the limit as a definite integral on the given interval. lim Ax [О, 6] 9 + X; i = 1 dx

A: The answer is found in step-2

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

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Q: Evaluate the integral. sec do %3D

A: According to guidelines we are supposed answer only first question if you want any particular…

Q: Express the definite integral using summation notation: 4 (3*) dx 1

A: We will convert the given integral into summation notation using Riemann sum ∫14(3x)dx.

Q: Evaluate the integral. (Use C for the constant of integration.) ] = 5 tan(x) sec³(x) dx

A: The given integration is: ∫5tanxsec3xdx To find the value of integration.

Q: Determine whether the integral is divergent or convergent.

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Q: Evalate the integral (tanx dx by using the reduction formıla of tangent fumction. х

A: Let u=tan(x). then x=tan-1u and  dx=tan-1u'du=duu2+1

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A: Integration and derivative

Q: Use integration by parts to prove the reductionformula.

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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: Use Romberg integration to evaluate the integral of f(x) = – between x = 1 and x = 3. Using 6…

A: As per the question we have to solve the following definite integral : ∫(1/x)dx from x=1 to x=3…

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: 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: Evaluate the integral. Use C for the constant of integration. 4dx

A: Given integral is- I=∫4dx9x3 It can be written as- I=49∫1x3dx=49∫1x32dx=49∫x-32dx

Q: Express the integral / rV1: V125 – 23 dr in terms of Beta function.

A: The solution is given as

Q: Evaluate the integral using formula #33 (from the 1-page differentiation & integration fom dx tan -…

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Q: Evaluate the integral of 3(sinx)3dx using lower limit of 0 and upper limit = pi/2.

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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

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: It is not possible of an integral of a function to be zero over a contour although the function is…

A: Yes it is possible,