O prove that : (2) DO 2x e dx a e +b where a, b >o

Q: (개) -3 dy 3yz

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Q: By using the substitution u = 4x +1, evaluate (4x + 1) dx %3D

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Q: O 2y = x In cx?

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Q: 6 If x=25eco, y=4tan8. Evaluate dy where B= Lrad Ans/-0.2647

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Q: If k> 0 such that O St the above 4* dx = 3 then k = 2ln 2

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Q: 3 Given that 3. e dx = e° - e, use this result to evaluate 3ex + 4 dx.

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Q: 5. Use geometry to evaluate (V4- x² dx 2 O 2n O 4t

A: Solution:

Q: Use the trapezoidal rule to find AT using the indicated value of n. 8 dx; n = 8 2x2 +2

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Q: а) Using an appropriate substitution, i) Evaluate fx*(1- x) dx. x2 Show that , (x-1)3 *+ In 2 . ii)…

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Q: Use a computer algebra system to approximate the it 2x 1I. * + 3y) dy dx

A: GIVEN DATA : The integral∫02∫x22xx3+3y2dydx Let the integral I=∫02∫x22xx3+3y2dydx First integrate…

Q: 0. Given that 15x V x2 + 4 dx = 25/5 - 40, what is 15uV u? + 4 du?

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Q: (a) If (In a] = , evaluate dx d [In x²] dx

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: The result is calculated as follows. '1 +5/8 dx 8_y13/8 . 13 = F(1) – F(0) - 0 II

A: Let I=∫01x5/8dx

Q: Let a be a constant. Given that 3? In(ax)dx = e1² ( 12 3 -23 find In a. 3

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Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: For a function y(x), the quantity dydx represents the first derivative of y. This quantity…

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: we know that lnmn=lnm+lnn similarly, ddxlncx=ddxlnc+lnx=ddxlnc+ddxlnx…

Q: 3 ex dx = e3 - e, use this result to evaluate Given that 5ex + 6 dx.

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Q: Sf(x)dと SgCx)dx, suppeat 9 Explain why SfC dx 7 goa) Counter ekample to やU8e a your claim .

A: Use substitute rule unless the integral can be simplified and directly evaluated. Counter example is…

Q: 25 - x2 In dx , if we let u=V 25 – x2 , then udu = - xdx. A True B False

A: On solving this we will get

Q: Prove that Ho Ge) =(-1) e" ď e dx 2. 2.

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Q: 10. What is 2ri 2 fo, h (z) dz?

A: curve C3 encloses points of singularity z=-2 and z=0 in clockwise and counterclockwise directions.…

Q: 42. (a) By completing the square, show that 1/2 dx T x² – x + 1 3/3

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Q: 70. Use the fact that (b*) = (In b) b* to prove that (ek*) = dx dx kekx. ||

A: Differentiation rules help to prove the required. The given fact helps to prove the required. Chain…

Q: Show that: (e) (VF) = 1 dx

A: Derivative of a function xn: ddxxn=nxn-1                               (1) Given function is: f(x)=x…

Q: Let g(u) = [" dx. Then dg 3 2+x2 du

A: The given integral is gu=∫3u312+x2dx. By applying the Fundamental Theorem of calculus,…

Q: 3 6. уд + уi —D 1, when x %3D 0, y %3D 4 0, у %3D 4 dx

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Q: Supposo that | FC) dx =13, fい)n -23, and gla)dx=35 2. fCx) drx = こxp(の J3fa) dx= C+fし),33J- 2.

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Q: Q2 by using Simpsons Rule method to find ,n=6 5 1 dx х 2

A: use sub interval for finding the integral.

Q: Chioma was asked to find (18x + 3)(6x° + 3x)° dx using u-substitution. How should Chioma define u?…

A: ∫(18x2 + 3)(6x3 + 3x)6dx We have to use u-substitution for the above function. To solve this, u is…

Q: 1 What is h(z) dz? 2ri C4

A: In this question, we evaluate the complex integral by using Cauchy integral formmula.

Q: Evaluate: / (In(2r – 1) – () + 25) da + 25 ) dx | Limits: [1, 6] Using Trapezoidal, n = 30

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Q: dy dx If y=e+19 then O 19e+19 O 4er+19 O 57er+19 O 3er+19 2er+19

A: Please see the answer in Step 2

Q: Prove that..

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Q: If IN = frNe-2= dx, show that IN +IN-1, and hence evaluate f r*e-2" dx = -

A: As per bartleby instruction when more then one question is given only one has to be answered. Please…

Q: 7. Use appropriate formula of geometry to evaluate the followings. L(lx – 3| + V36 – x²)dx b. L(2x +…

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Q: Determine whether the statement is true or false. If it is true, explainwhy. If it is false, explain…

A: Given, ∫04xx2-1dx=12ln(15)

Q: 53 what is 13' 3 Given that f(x)dx = f(v)dv?

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Q: Let f(0) = 6 and ƒ(1) = If ) dx In then a =? %3D 8.

A: given that f(0)=6 and f(1)=94 and ∫01f'xfx dx=lna8  find a

Q: Evaluate the defin c12 4e 4*dx 3.

A: Given:     Integration of 4e4x from 3 to 12 limit.

Q: 5. For what value of k, k> 0, does (6kx-2k) dx = -k³ ? о 1 02

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Q: UCe the Vmit de fi miおもn of rhc aefrile へとgral, im ; fcxi)x - 5fしょsdx」 to prove hat ハう fex) dx= -…

A: Prove ∫abf(x)dx=-∫baf(x)dx using the limit definition of the definite integral as follows. By limit…

Q: - 7x)4 dx Using an appropriate substitution, evaluate: B

A: The given integral: I=∫x6-7x4 dx

Q: Q1: what is on (3x) SI2 dx x2

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Q: using an appropriate su OTE: Enter the exact answer. 4 | - | dx - 4 (1 – 2x) ¹ +C

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Q: 3 Given that ex dx = e³ – e, use this result to evaluate 7ex + 4 dx.

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Q: f (г, у) — In(ax + by) a, b ER af Land 1 Find Ja 2. Find and a f -and 3. Find dxðy дуда

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Q: 5. Use Green's Theorem to evaluate (y – 42) dx – (2+x²y²) dy where C is shown below. y (5,10) 10

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Q: Suppose that o f(x) dx = 3. Find , f(x) dx if, %3D

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