117. If f is a continuous function, find the value of the integral f(x) dx I = f(x) + f(a – x) by making the substitution u = a – x and adding the resulting integral to I.

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

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Q: Consider the graph of the function f(x): YA y= f(x) -2 4 6. 8 Evaluate the following integrals by…

A: To find the following intergals in terms of area (a)∫02f(x)dx=area of trapezium=…

Q: Let a be a constant. The indefinite integral F(x) = ] ax+3 dx equals [F].

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Q: Evaluate the integral of ((x dx) / (x + 1)^8) from 0 to 1.

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Q: Use the Simpson's Rule to evaluate the integral fx sin(x)dx. W/H N/" N /H 02/ O

A: We have to evaluate the integral ∫0πxsinxdx. Here, a=0 and b=π Let n=2 Hence, Δx=b−an=π−02=π2.…

Q: To evaluate the integral f(x)dx, , the substitution u='g(x) is used. Thus if g(x) = x+4 then dx =

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Q: Consider the functions given.evaluate the integrals

A: First we try to write the given function using the mentioned functions.

Q: (d) dx (x + 1)² 1

A: Given integral, ∫1∞xx+12dx Need to solve the integral, to find the given integral is converges or…

Q: Q2) Find the integral of: f*,6 tan*x dx

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Q: If f is continuous and f(t) dt = 18, find the integral Answer:

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Q: If - 1 | f(2)dr = | f(x)dæ + / f(=)dr - /. f(æ)dx, what are the bounds of integration for the first…

A: I have used the properties of integration

Q: Evaluate the integral f [[ - Y sin(x²)dxdy.

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Q: Use the specified substitution to find or evaluate the integral. (Use C for the constant of…

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Q: Evaluate the integral. (Use C for the constant of integration.) S. x² – 16 dx x3

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Q: Set up the integral to find the length of the curve f(x) = V1 – 2? for 1/v2 <x < 1.

A: Please see the answer below.

Q: Use the specified substitution to find or evaluate the Integral. (Use C for the constant of…

A: The given integral is ∫x-5x+8dx. The main objective is to evaluate the integral by the substitution…

Q: 18. In each part, evaluate the integral, given that f(x) = (2x, x≤1 x>1 2, (a) forex f(x) dx (b)…

A: 18.fx=2x,x≤12,x&gt;1

Q: let b be a constant. use definition to find  (integral 0 to b)(x+1)^2 dx.

A: Given: The expression of integral as ∫0bx+12dx, where b is a constant, To evaluate: The value of…

Q: Sx²e2x*dx `x²e?

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: A. Evaluate the following indefinite integrals using the Power Rule: 1. SE Va dx 2. S dx 3. S(-Vx +…

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Q: To evaluate the integral f(x)dx, the substitution u= g(x) is used. Thus if g(x)= e* then dx =

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Q: +00 dx II. Evaluate the improper integral x(In x)²

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Q: Evaluate the integral using the given substitution. (Vx cos (x3/2- 4) dx

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Q: Find the integral of f(x) = e- sinh(x) between 0 and 1.

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Q: Use the specified substitution to find or evaluate the integral.

A: Consider the provided integral, ∫01 dx23-xx+1 Evaluate the provided integral. ∫01…

Q: Use substitution to find the indefinite integral

A: Given ∫1xlnxdx

Q: ~2 .4 x* +1 dx 1 J1

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dx,…

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

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Q: Let F(x) be an antiderivative of a function f(x) and let a + 0 be a constant number. Express the…

A: Given that F(x) be an antiderivative of function f(x) We have express  the indefinite integral…

Q: Q2/ Find the integral of, 1/n f(x) * cos(3x) dx , for f(x) =1 on [-n, 0] and f(x) on [ 0, a] (using…

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Q: Evaluate the following integral along the indicated curve Where c is: y = -x ^ 2 (parameterize it)

A: We will find out the required value.

Q: +00 dx Evaluate the improper integral x(In x)²

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Q: Use the Comparison Theorem to determine which of the following integrals converge. (i) arctan x dx…

A: Use the comparison theorem to identify the given integral as convergent or divergent.

Q: Let a be a constant. The indefinite integral F(x) = dx equals (F]. ax+3

A: Given integration is  F(x) = ∫dxax+3

Q: If f is continuous from the integral 0 to 9 of f(x) dx = 20. find the integral 0 to 3 of x f(x^2)…

A: Given. ∫09f(x) dx=20 To determine. ∫03xf(x2)dx Let x2=u Differentiate the function x2=u.…

Q: f(cos*x- sin *xkx *a

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Q: b. d. 1 dx x4 ° 1 dx f. | h. (y³ – 3y²) - 8

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Q: Evaluate the integral f 9(√x² + y²) dxdy.

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Q: x² In x dx 2. 0.

A: we have to evaluate the following improper integral.  For this we can use integration by parts

Q: 8. dx Evaluate the improper integral if it exists O.

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Q: Evaluate the following indefinite integral. Show all intermediate steps. fx√x+1 dx

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Q: Define the following improper integrals integral -1 to  1 f(x) dx

A: Given integral is,

Q: Q23: Find the integral of f x In(x) dx.

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

Q: Evaluate the indefinite integrals, use the substitution when appropriate. a) S(e5- VE +) dt b) S cos…

A: a. Evaluate the given integral as shown below: ∫ t5-t+1tdt=∫ t5dt-∫tdt+∫1tdt…

Q: Evaluate the integral / f(x) dx, where S-x - 1 f(x) = l-VI - x² if – 1< x < 0 if 0 < x < 1 Hint:…

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Q: For what values of  a is ∫0∞ eax cos x dx convergent? Evaluatethe integral for those values of a?

A: ∫0∞eaxcosx dx Now, ∫0∞eaxcosx dx=limt→∞∫0teaxcosx dx=limt→∞eaxa2+1acosx+sinx0t    ∵∫eaxcosbx…

Q: Use the specified substitution to find or evaluate the integral. (Use C for the constant of…

A: See attached file for a step by step explanation to find the required Integral.

Q: Evaluate the following integral or show that it is divergent. 0 -√x VX dx

A: Explanation of the answer is as follows