19 The value of f(x) dx by using 2-segment Simpson's 1/3 rule is estimated as 702.039. The 3 estimate of the same integral using 4-segment Simpson's ½ rule most nearly is 702.039 a. + [2 f(7) - f(11) + 2 f(15)] 2 b. 702.039 + [2 f(7) - f (11) + 2 f(15)] c. 702.039+ [2 f(7) + 2 f(15)] d. 702,03⁹+2 f(7) + 2 f(15)]

Q: 2. . If f(x) dx = 4 and 3g(x) dx = -9, evaluate [² [3f(x) + g(x)] dx

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Q: 14 6,¹ 3 Suppose f(x) dx 3 S f(x) dx = [ 14 = 15. Find

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Q: x3 1+x² dx

A: Note : according to our guidelines I can solve only one question, please reroute the remaining one.

Q: 12 If [" f(x) dx = 19 and ' [₁ f(x) dx [R²F(x) f(x) dx = 4, find the following.

A: We can answer the question as below using the properties of definite integral.

Q: 57. Verify that S2 yields the exact value of | (x – x³) dx.

A:

Q: 8 Suppose we would like to approximate √3³ f(x) dx using six (6) midpoint rectangles of equal width.…

A: To calculate the width of each rectangle when approximating an integral using the midpoint rule, you…

Q: Let (a) 10.5 3.5 ・6.³.5 P f(x) dx = 9, [ r(x) dx = [ 3.5 10.5 a £10.5. f(x) dx = 4, and (b) (8f(x) -…

A: Given,

Q: 11. f VI+x6 dx 3.957736

A: Given definite integral is ∫121+x6dx. Now using Ti-83, given the following command. 1. Click MATH…

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: Find 9 JBS if [3f (x) - g (x)] dx = i 9 9 frode = 2 and 1200dx = 50 [80 (x) dx g (x)

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Q: | 1/(x3 – 8) dx

A: To evaluate: I=∫1x3-8dx  I=∫1x3-23dx We know that x3-a3=x-ax2+ax+a2 ⇒I=∫1x-2x2+2x+4dx

Q: lim x→0* √√x ln x

A: The given limit is

Q: 7. Let f(x)=64x² ln (2x) −16x¹. Findƒ(e)-f(€) 2

A: NOTE: Refresh your page if you can't see any equations. . take x=e

Q: (a) Estimate the area under the graph of f(x) = 2 + 4x from x = -1 to x = 2 using three rectangles…

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Q: 3. Use substitution/general power rule to find the indefinite integral and check your answer by…

A: Given integral ∫4x( x2 + 5 )6dx

Q: 10 6. Evaluate -dx. (x – 1)(x² + 9)*

A: Given integral is We will evaluate the integral by using the concept of partial fraction…

Q: Let T1 : R" → R* and T2 : R* → R" be linear transformations. Prove that for all k e R, and ve R":…

A: Idea: using definition of linear transformation  T(kv)=kT(v)

Q: 4. x(x² – 1)² dx

A: Solution:

Q: 8. (a) Show that (b) Evaluato 1/3 3 √1+9x² -4x4 dx dx = ln(1 + √2).

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Q: Suppose Then 6 Sº f(x f(x) dx 10 [₁ f(x) f(x) dx = A 5 and 10 [ f(x) 6 f(x) dx = 7.

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Q: If | f(x)dx=12, what is the value of f(6- x)dx?

A: Let f(x) be continuous on [a, b] , where a=0 , b=6 Suppose there is a function F(x) such that f(x)…

Q: Suppose F(x) is between 4 and 8 for x in [3,12]. What is the largest that · 12 L" F (x) dx can be?

A: given that function F(x) between 4 and 8 for x in [3, 12] we have to find the largest value of…

Q: Given L f(x) dx = 16 and i g(x) dx = 8, Evaluate the following I [2f(x) - 3g(x)] dx

A: Given query is to find the value of the indicated integral.

Q: If f (x) = 3x + 5 and g(x) = x³,finc а. (f + g)(x) b. (f/g)(x) c. f(g(x)) с. d. (f°f)(x)

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Q: 11

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Q: -11 If " f(x)dx = 1 ; S,f()dx = 22 find f" fx)dx. Eiles

A: