It is not possible of an integral of a function to be zero over a contour although the function is not analytic inside the contour.

Q: Describe two ways for an integral to be improper.

A: The definition of an improper integral,  An improper integral is a definite integral that has either…

Q: evaluate the integral of xe^(-x) show all work

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Q: I need to evaluate the follwing integral or state that they diverge

A: The given integral is ∫02dxx3

Q: State the Comparison Theorem for Improper Integrals. As well, use it to determine whether I+2 dr…

A: The comparison test states that if limx→∞f(x)g(x) is finite and non-zero, then ∫f(x)dx and ∫g(x)dx…

Q: Use the limit form of the definition of the integral to evaluate the integral, (3 – 2x) dx. Show all…

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Q: Сompute 1. f dx, where f(x)=|x|.

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Q: Explain why the limits of integration are changed when u is substituted for an expression in x in a…

A: The limits of the integration are substituted at the end of the integration when the function is…

Q: Evaluate the definite integral by the limit definition

A: Here,

Q: Use the definition of integral to express the integral as a definite integral over a given interval.

A: (1). The given expression is: limn→∞ ∑i=1∞ xi ln1+xi2 ∆x     over  the interval [2, 6]

Q: The area bounded by the small loop of the line limaçon r= 1-2sintheta is given by the definite…

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Q: Suppose fis continuous on [a, b]. Which of the following is not a definite integral?

A: Given,           Suppose f is continuous on a,b.

Q: Use the form of the definition of the integral given in this theorem to evaluate the integral. [²4x³…

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Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A: Given integral is ∫121t-3-8dt.

Q: Express the limit as a definite integral.

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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…

Q: |In (x)| 1+x2 8

A: Divide the given integral into two parts and then calculate the each integral.…

Q: Evaluate the indefinite integral. Show work!! dy (1-ev)?

A: Answer

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. (x2 +…

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Q: Evaluate the definite integral exactly, using the Fundamental Theorem. dt dt 3= eTextbook and Media…

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Q: to express the integrals as limits of [ f(x) dx (b) [f(x) dx

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Q: What is the definite integral of a function ƒ over a closed interval [a, b] ? When can you be sure…

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Q: Evaluate the indefinite integral using u-sub. Show all work. 2x+4 dx J 3-2x2

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Q: Suppose f is an odd continuous function whose mean value (with respect to integral) on the interval…

A: Given:           ∫25(3f(x)+K)dx=34

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

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Q: Using only the definition of RS-integral, evaluate |x* d[x}.

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Q: Use the form of the definition of the integral given in the theorem to evaluate the integral.

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Q: Use the Fundamental Theorem to evaluate the definite integral exactly. | = 3xdx

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Q: Evaluate the integral from 0 to infinity of 1/[x2+5x+4] or show that it diverges

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Q: Evaluate the integral. inegral  ax / (x2 - bx ) dx

A: Consider the given integration as I=∫axx2-bxdx⇒I=∫ax-bdx

Q: f(x)=sin(x)/x_between 0 and 1 using Trapezoidal

A: fx=sinxx Trapezoidal rule fx≈h2fa+2fa+h+fa+2h+---+fb a=0, h=0.05 and b=1

Q: Use the form of the definition of the integral given in this theorem to evaluate the integral.

A: Topic:- definite integration

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

A: Given a statement

Q: YA y= f(x)

A:

Q: PitgXL

A: We will use the fundamental theorem of integral calculus and the Newton-Leibnitz theorem to find the…

Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

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Q: Using only the definition of RS-integral, evaluate x* d[x].

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Q: Let a and b be non-negative real numbers. Provide an example of an improper integral of the form…

A: Given problem :-

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. (x2 4x…

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Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. 6. (x2…

A: Given,            ∫16x2 - 4x + 7 dx

Q: The integral of x-Inx with respect to x is,

A: Given,             The integral of x2lnx with respect to x.

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: What conditions have to be satisfied to use the Integral Test?

A: Here we need to describe the required condition for using Integral Test.

Q: Verify the Mean-Value Theorem for integrals, for the function f(x) = x² + 5 [0,3]- on

A: We need to verify the Mean-Value theorem for integrals, for the function : f(x)=x2+5      on  [0,3]

Q: Use the Simpson's Rule to evaluate the integral f x|x²dx

A: Please post the multiple questions separately.Here I answered 1st question  as per our policy.

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…