Which of the following properties of definite integral is INCORRECT? -2 3 f(x) d=F(2) – F(1)} 3 2 2 - ..... .......... S (2)dx = - [" f(x)dæ + g(x)]d® ..... ..... ... ..............

Q: 1. Using properties of definite integrals, given f(x)dx = 10 and | g (x)dx = – 2, evaluate 2 6. a)…

A: (a)∫26-f(x)+g(x) dx  = -∫26f(x) dx+∫26g(x) dx = -10 + (-2) =-10-2=-12∫26[-f(x)+g(x)] dx =-12

Q: 12. Now, recall our discussions with respect to indefinite and definite integrals, and do the…

A: The answer is found in step-2

Q: The anti-derivative of x" is xn+1/(n + 1) for all values of n. The integral of csc x equals -In|csc…

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Q: Q2 - Evaluate the following integrals sinh'x cosh°x

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Q: Given that 3 <f(x) < 6 for -7<x< 4, use a property of definite integrals to find an interval in…

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Q: 11. Rules of Definite Integrals: If f(x)dx = 12, S." f(x)dx = 6, and "f(x)dx = 4, find the…

A: Given that: ∫05f(x) dx=12∫512f(x) dx=6∫812f(x) dx=4

Q: 49 What is the value of the definite integral 21x -4 dz? Provide your answer below:

A: To evaluate the the given integration .

Q: 1. Evaluate the following integrals using appropriate methods and simplify your answers. (a) ² dr

A: We will answer the first question as you didn't mention any. Please resubmit the other questions…

Q: B. Evaluate the definite integral using the Simpson's rule, giving the answer correct to 3 decimal…

A: Topic- Integration

Q: 9. √x SOL -√√x dx

A: We will solve the given integral using simple Integration rules.q

Q: Given the function graphed below, evaluate the definite integrals. 4+ 3 2 3. -1 -1 4 5 -2 -3 -4 |…

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Q: Given the function graphed below, evaluate the definite integrals. 4- 2- -1 2 4 5 6 -2- -3 -4+ of…

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Q: The value of the definite integral is Select one: O none of the others 45 6 30 -30 [² (3x² - 2x (3x²…

A: Topic = Integration

Q: Q3/Find the value of x If the approximation of the integral f f(x) dx by trapezoidal method is given…

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Q: 9. Use the properties of definite integrals to find |f(x) dx for the following function. 4 8x + 1 if…

A: Accoding to condition of f(x)  devied it in two part where function changes.  Then simply integrate.…

Q: How many evaluations of the function f(x) = (1+ 2x)¬1 is needed in order to approxi- mate the…

A: Given: fx=1+2x-1   To determine: The number of evaluations of the given function needed to…

Q: Given the function graphed below, evaluate the definite integrals. 4+ 3 -1 3 4 6 8 -2 -3 -4 | f(x)dx…

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Q: Find the value of∞ If the approximation of the integral f f(x) dx by trapezoidal method is given by,…

A: We have to use the trapezoidal formula to approximation of integral  ∫01f(x)dxThe approximate value…

Q: True or False: The definite integral is equal to Select one: O True False 1² (x² + 3e*)dx [²x²dx + 3…

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Q: - Using the integral definition of gamma function show that T(7) = 61(6)

A: Integral definition of gamma function is Tx=∫0∞tx-1e-tdt . Put x=7 in Tx=∫0∞tx-1e-tdx and simplify…

Q: 7 Use the properties of definite integrals to find f(x) dx for the following function. 2 4x + 1 if…

A: We will solve the problem

Q: Observe that f is a linear function; what kind of function is A? Using the formula for 4(x) that…

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Q: The functions f and g are integrable and f(x)dx 2. f(x)dx 4, and g(x)dx= -3. Find the values of the…

A: Given, ∫24fx dx=−2,∫27fx dx=4 and ∫27gx dx=−3Concept used:1. ∫aafx dx=02.  ∫abfx dx=−∫bafx…

Q: 5. Evaluate the integral A by Simpsons rule with 2m = 8, and compare your result with the exact…

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Q: 50. Suppose f has absolute minimum value m and absolute max- imum value M. Between what two values…

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Q: (x S+ 3x? - 4 ) dx 12

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Q: 2) Use the properties of the definite integral to find the given integral, if possible, given that…

A: As per our guidelines, I can answer maximum three subparts of a question. To know rest, please…

Q: B. Evaluate the definite integral using the Simpson's rule, giving the answer correct to 3 decimal…

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Q: How to evaluate this definite integral: ∫[e^3, e]  (3((ln(x))^3) / x dx

A: The definite Integral will be solved by substitute method

Q: What values of a and b maximize the value of the definite integral | (x - x²) dx a a = b =

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Q: Given the function graphed below, evaluate the definite integrals. 3- -1 6 -2 -3 f(x)dx = | =|…

A: the given graph is: we have to find: ∫01f(x) dx  and  ∫19f(x)dx

Q: 6. Evaluate the following definite integral using the fact that sin x dx = 1. S. | (2 sin x + 3) dx

A: ∫0π2(2sinx+3)dx Take integral for each term ∫0π2(2sinx+3)dx∫0π22sinx dx+∫0π23 dx2∫0π2sinxdx+3∫0π2dx…

Q: Use the properties of definite integrals to find f(x) dx for the following function. 2x + 5 if x5…

A: Given that, We have to find : ∫46f(x)dx

Q: Given the function graphed below, evaluate the definite integrals. 4+ 3 2 1 -1 7 -1 -2 -3 -4 1 S.³…

A: Need to find out the definite integrals.

Q: Which of the following can be evaluated directly by the Power Formula of Integration x² dx (x3 +x +…

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Q: hich of the following definite integral has the greatest value? (A 2+xdx .5 B J. V6-xd В C sin x dx…

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Q: 8) Evaluate the indefinite Integral S x ³ √√₁₁ + x ²4 dx

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Q: Given the function graphed below, evaluate the definite integrals. 2 3 4 5 6 7 8 -3 -5 [²ƒ(z)dz = −5…

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Q: Find the value of the constant C for which the integral 6C x² + 9 dx X + 3 converges. C = Evaluate…

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Q: Evaluate the definite integral. '7 l'e e-x dx

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Q: The value of the definite integral fm12 √ex - 9 dx is in the form F(b) – F(a), where a In 9 and b…

A: We have to solve given Questions.

Q: Q3/Find the value of x If the approximation of the integral f f(x)dx by trapezoidal method is given…

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Q: 1. Problem on the evaluation of real definite integral by contour integration: roo log x t log b dx…

A: Here we have to evaluate the real definite integral by contour integration.

Q: b. False. The interval of integration [-1, 1] contains 0 at which function and the above theorem…

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Q: 2 58 n lim dx !! (n+1)? j=1 and the value of the integral is

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Q: Given the function graphed below, evaluate the definite integrals. 4- 3 2- -1 3 5 -2- -3 -4- f(x)dæ…

A: The definite integral  ∫03 f(x) dx  is the area under the give curve from 0 to 3.

Q: In this problem you will calculate 2x dx by using the formal definition of the definite integral:…

A: The procedure described in this question is called Finding the Riemann sum and then taking it's…

Q: The integral dx cannot be evaluated by finding an antiderivative. Find a lower bound for the integer…

A: We will use error formula for trapizoidal

Q: 1. What is F(x)?Define it from your understanding. Is it the same as f(x) 2. What is the other term…

A: In an integral , F(x) represents a function whose derivative is f(x) F(x) and f(x) are not same.…

Q: 2. Use only the following given values of definite integrals to find the other definite integrals…

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