For any natural number m, evaluate 1/m +x")( 3m 2m 2m +x 2x +3x" +6)"* dx, x > 0. m X

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A: GIVEN: f(x) = 1 + cos (x/2)

Q: Q3:- find the erea of the shap by the order 1- SS dydx 10

A: Please refer the attached image for complete solution.

Q: Sin (n+))x Conv. unif nナノ on Prablem (5) Is the senies

A: The given series is: ∑n=1∞sinn+1xn+1 The given interval is: 0,π

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A: We have to find

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A: Given,  ∫02x3dx, n=4

Q: To evaluate the integral 1. 7 64 + x² -dx,

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Q: If f(2) = cosh (In a), then f'(7) = %3D Your answer should be rounded to the nearest whole number if…

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Q: figure th

A: 1) Here we have to find the ∠RST=?

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Q: If f(z) = cosh(In z“), then f' (7) = %3D %3D Your answer should be rounded to the nearest whole…

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Q: Expand in ascending powers of x up to and including the term in x. 7x assuming x = 25 estimate v13…

A: Given: 1+x1-7x12

Q: Evaluate the indefinite integral. бх + 7 +C. || x2 +1

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Q: 8. Use Simpsons' rule to numerically integrate for the n = 6, case f (x) = x on the unit interval,…

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Q: Prove using the INT. For all positive integers k, cos x = xk has a solution.

A: To Prove: For all positive integer k, cosx=xk has a solution using Intermediate Value Theorem.…

Q: 1. Show that cosh 4x = 8cosh“x - 8cosh? x + 1 .

A: Given problem:- Show that cosh(4x) = 8cosh4x - 8cosh2x + 1

Q: Using the substitution u = 2x – 1, prove that - -3 8 dx 1 (2x-1)3 25

A: The given integral is ∫13x(2x-1)3dx Put 2x-1=t⇒2dx=dt when x=1 then t=1 and when x=3 then t=5 So,…

Q: uce this to evaluate In xdx

A: The general formula for integration of xnlnx is , ∫xnlnx.dx=xn+1.lnx-xn+1n+1n+1+c Now we have to…

Q: Evaluate the integral. 24. '8 -2/3 dx

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Q: In (a le) secx ((2- sec²x) " sec (3А - x) to be integrable using the formula What should be the…

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Q: -2 -In x SLy e dz dx dy O 7/24 O 7/48 O 5/48 O 47/24

A: We have to find the integral.

Q: tain we and tangent together. 6. у %3D (х — 1)? + 1, (1, 1) 1

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Q: Evaluate the indefinite integral. 7 dt 7 (t + 4)"

A: Given,            ∫7t+47dt

Q: Suppose that 0 <q<pand that F(h) = L+0(hP) show that F(h) = L+0(ha).

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: If u= In x, then 1- (In x)2 dx=?

A: Find your answer below

Q: Use the error bound to find the smallest value of N for which Error(SN) < 10-º. 9x4/3 dx (Give your…

A: The given integral is ∫169x43dx. Here fx=9x43  for  1≤x≤6. The errorSN denotes the error bound…

Q: 8. Use Simpsons' rule to numerically integrate for the n = 6, case f(x) = x on the unit interval,…

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Q: 26) ) Show that the reductión formula for 1ー2 Sec" ndx = Sec atan n t n-2 n-- n-1 ) Hence use tta…

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Q: The value of c of fo-2- in the iterval .D such that rio--E) OA 3 OB. -3 OC 3 O0. 3-

A: c = 3explanation is given in below step

Q: evaluate using the appropriate method or combination of methods.

A: We will need by parts method with

Q: 2. Use the Intermediate Value Theorem to show that 2.x 3 - if – 3 0 has a zero on the interval [-2,…

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Q: fle) sinzdz Compute

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

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Q: 23+dt (4+3 Co+ 3+)5

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Q: Prove that x" dx „n+1 + C, n + 1 for n + -1.

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Q: Find the chara derieti'k palynow ral of f the aatrcx 2. 1)

A: Answer is mentioned below

Q: © Find the singular value deomposition of the matix I- A =

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Q: 4. Show that In sin 6 d0 = – n 2 by applying the mean-value principle to In |1+ z| for |2| <r < 1,…

A: ∫0π2logsin(θ)dθ=12∫0πlogsinθdθ                         =12∫0π2logsin2θdθ…

Q: Show that dx = x² – 8x In (7 + 4/3). -

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Q: If u In x, then 1-(In x)2 dx =?

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Q: Find the lenegth of the cunde 312 2 from x=o to -

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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: Evaluate the definite integral. 7 ° In(3t)dt =

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Q: Find an expression of for y = 2*ev*, Hint: (a*) = a* . (x) · In a

A: We can find the derivative as below

Q: let 9: R-R be given by grs) - Sin (는) %3D %3D dis prove that se second hind has prove of dis…

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Q: Evaluate the improper intergal 1 -00 dx using the residue (x² + 16)3 theorem. 00 2

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Q: Use the Simpson's 1/3 rule with n = 8 to estimate: cosx

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Q: Use symmetry to evaluate the following integral  (x^3+2x^7)/(x^6+4)  [-3,3

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Q: 3-Expand In [x? sin³ x /vx2 +1]

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Q: Prove that 1- cosh -1 x= In(x+ Vx- -1 1 x+1 2- coth -In x-1 X = - Vi+x? .2 1 3- csch -1 x = In(-+

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

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