(-1, –2 < x < 0 1, 0

Q: 5. (a) Use integration by parts to find f xe-3x dx. +00 -3x (b) Determine whether the improper…

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Q: Evaluate the indefinite integral S- dx 3x² x³√x6-1 O 3+C sec-1 +6 O sec-1x3 3 + C ec²¹x² + C sec 3…

A: SOLUTION-

Q: (5) Find the indefinite integral (a)fVtan x sec'dx aun 2x sec' 2xdx sin x (c)) cos'x 1 cos-de

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Q: Evaluate the definite integral S (1+ 2x) dx using Riemann sum.

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Q: n, ]x| fn (x) = - 2m 0, x > 2n | fn (x) cos x dx lim Calculate its limit. What happens if the limit…

A: Write the integral as limn→∞∫-11fnxcosx dx=limn→∞∫-1-12nfnxcosx dx+∫-12n12nfnxcosx dx+∫12n1fnxcosx…

Q: Q3) Use Riemann sum to evaluate the definite integral: 2 | (2x + 1)dx where n = 0.4

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Q: A definite integral Evaluate In x dx.

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Q: One of the correct steps to evaluate x2Inx dx to yield the correct integral x³Inx A x² dx 3 O ---fa…

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Q: 4. fsin (In x)dx

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Q: 7. Let 3 hox) dx = - 108 -le hex)dx = 32 Use the given definite intcgrals above to evaluate euch…

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Q: integral of (1/(1-x)^3)dx  from 1 to 3   and  integral of (1/(1-x)^3)dx  from 3 to infinity

A: The solution are next step ..

Q: 5) Approximate x²-1|dx with a right-endpoint Riemann sum using four equal subintervals.

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

Q: solve the integral: I3=integral limit from 0 to positive infinity 1/(4e3x+7) dx

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Q: 3. Does the improper integral 2 dx converge? et +e-*

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Q: - e*) sinh x + e* cosh x + ex In the indefinite Integral in(cosh x + ex). A In(cosh x + e*)- sinh x…

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Q: integral from -5 to 4 of absolute x^2-4 dx

A: ∫-54x2-4 dx

Q: hat are the new limits of integration after applying the substitution u = 6x + x to the integral /…

A: Given query is to find the limit after applying the substitution.

Q: 02:- By using integration by part, find :- (Choose two only) 2-f Inx (x') dx

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Q: sin(x) dx =-x² cos(x)+2 cos(x)+ 2 x sin(x) + C e* s in(x) dx= 1 cos(x) + e* sin(x)+ C e*

A: Topic = Integration

Q: 15. Indefinite Integrals (Part 1) а) -+ cscxcot x dx 2 cosx--sinx+4csc². 3 b) 1 + sec² x dx 1+x2 c)

A: topic - indefinite integral

Q: integral of sqrt(9-x^2)(x)dx. limits are from 0 to 3

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Q: sec?x dx 1- tan x b. Determine whether the integral converges or diverges.

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Q: sinh x tex cosh x + ex In the indefinite Integral in(cosh x + ex)- sinh x tex (A) cosh x + ex B sinh…

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Q: the point of discontinuity on(0, co), the Fourier Sine integral converges to: None (**) + f(x¯)] **)…

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Q: Explain why the improper integral (x + 3) sin(x) dx L. (x² + 1)(x² + 4)² is convergent. 8

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Q: Evaluate the integral -21 cos(-2t) dt Note: Use an upper-case "C" for the constant of integration.

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Q: solve the integral: I2=  integral limit from 0 to 4= 1/((x+1) squar root of 2x+1) dx

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Q: integral from 0 to 1 of square root of (1- square root of x) dx

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Q: 12. Let a and b be non-negative real numbers. Provide an example of an improper integral of the form…

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Q: Double of Integration of square root of 25-x²-y² with respect to x bounded by (0,3) and with respect…

A: The given integral is

Q: * Using integration by parts, the integral sec³dx is equal to 1 1 - secxtanx +In|secx +tanx| + C 2 1…

A: Use by parts method of integration

Q: In the indefinite Integral Sin(cosh x + ex)- integrand? A In(cosh x + ex) B sinh x + ex In(cosh x +…

A: The given function whose integral is to be found is called the integrand.

Q: 5) Evaluate ehe integral (use c fos Ane constant of integration. tan'cx)cos x) dx

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Q: sinh x tex cosh x + ex In the indefinite Integral Sin(cosh x + ex)- sinh x tex A cosh x + ex sinh x…

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Q: evaluate the indefinite integral 3+ -dt. Use C for the constant of integration.

A: Given : ∫3 + 1t61t2dt

Q: x° sin(x³) In(4 + cos(x³)) if x 10° ya. 00 Determine whether or not the improper integral dx…

A: We have to use comparison test here.

Q: Determine h and N to approximate the integral e- dt within an accuracy of G = 10-5 using the (i)…

A: ii)  Equation is f(x)=exp(-x2).The value of the table for x and y x 0 0.25 0.5 0.75 1 y 1…

Q: 3 sin 2t 1. If f (x) = Jx Ve2+Int dt, find f'(x) Jx Jt?+Int

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Q: 11)By using Tabular integration solve the integral f x³ 2* dx A)Sx³ 2* dx = x³, In 2 2* 3x2 2* 2* +…

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Q: 3 integral, if exists : (5 – x)³ dx 3 - 8.

A: In the question we have to find the definite integral.

Q: f(x) = _-2x² – 6x – 4 х2- х - 2 Holes: Vert. Asy: Hor. Asy: x-int: у-int: Domain

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Q: sin (nx + 3) f (x) V is convergent point wise to zero function. n- 1 صواب ihi

A: True

Q: Use Romberg integration to approximate √² 2x² + x − 1 dx. Compute the Romberg table until Rij-…

A: The Final diagonal element is always consider the best estimate of the integral  I=∫abf(x)…

Q: This question has several parts that must be completed sequentially. If you skip a part of the…

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Q: O- O: If the improper integral converges, Show and find its value or ex plain Why it diverges: dx X…

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Q: isolated singular point 1. z/((z^3)+z) 2. exp(tan(1/z)) 3. (1/(z^2)) * exp(1/(z^2)) z=4 is apole of…

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Q: In The value of the definite integral flm 12 √ex - 9 dx is in the form F(b) - F(a), where a JIn 9…

A: To evaluate: ∫ln⁡9ln⁡12 ex−9dx Let I =∫ln⁡9ln⁡12 ex−9dx Given: ∫ln⁡9ln⁡12 ex−9dx = c3-dπ Let ex−9=…

Q: Evaluate the definite integral S (1 + 2x) dx using Riemann sum.

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Q: O- O: If the improper integral converges, Show and find its value or ex plain Why it diverges: xa ix…

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Q: Use integration by parts to evaluate the definite integral: ∫3se^-4s ds with an upper limit of -0.9…

A: A=3∫abse-4sds , solving A where a,b are upper and lower limits as per questionIntegrate by parts…