Using integration by parts, Then k is? (a)-1.5136 [²x³ cos(x²) dx = k - [*²x sin(x²) dx (b)-1.1365 (c)-1.3651 (d) - 1.6513

Q: Use Gaussian Integration (4-point form) to approximate | x?sin(x)dx

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Q: ln(r^6s^5 5√r^8s^9) is equal to A ln r+B ln s where a=? b=?

A: lnr6s5 r8s95Concepts:ln (m n )= ln(m)+ln(n)ln am=m ln aam*an=am+namn=amn

Q: dp Find dx given p(x) = (sin?(3x))(3x²-4*)

A: As we know that; The chain rule: fgx'=f'gx·g'x The Product rule: f·g'=f'·g+f·g' The Power rule;…

Q: (i) Use the chain rule to show that -3x = (In 3)32 dx Hint: use the fact that 3 = eln 3ª (ii) Use…

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Q: cosh (x – 3) dx 2 '8 – cosh² (x – 3) х In x dx

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Q: (a) Find an approximate value of S x*e*dx (b) Solve for -dx x²+9 xp

A: Here we have to find the value of given definite integral.

Q: Numerical Integration: 2 1 1. 2. =dx X 5 (2x² – 3x) dx 0 2

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Q: 4 12d2= -dx = x² - 1 (A) B D 4 ln x² - 1| + C 2 ln+C 4sin ¹x + C 4tan ¹x + C

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Q: PROBLEM SOLVING: Evaluate the following integrals | 1. Jdx/(x-1) ² 2. JV (4-x) dx 3. (9-x) ¹/3 dx…

A: Since you have posted multipart question we'll do first three parts of the question. If you want any…

Q: using T= πT integration TT/2 dn= *2 O cos x cosnx dx

A: We know that: cosAcosB=cosA+B+cosA-B2∫cosaxdx=1asinax+C

Q: –1/2 | (x (x² + x) + 4)dx.

A: Given,            ∫04x-1/2x2 + x + 4 dx

Q: Given | f(x) dx = 0 and f(x) dx = 11, evaluate -1 » Lwa. (a) f(x) dx. 1 (b) f(x) dx – f(x) dx. 1 (6)…

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Q: 2 sin -(x/6) dx Evaluate the integral 2. 36-x 2. r(sin sin (x/6) dx 2. V36-x?

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Q: x3/8 |dx (assume x > 0) 4. +

A: ∫xndx=xn+1n+1+C∫1xdx=lnx+C∫exdx=ex+C

Q: What is the difference between net area and total area?  Which does the definite integral of f(x)…

A: Given problem:- What is the difference between net area and total area? Which does the definite…

Q: sin? 6, determine a reduction formula for the 5 By the substitution x = integral 2(1- x)2 dx. Hence…

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Q: dx x (In² x – 6 In x + 10) -

A: The Answer is:      Result = arctan ( ln x - 3 ) + C

Q: |In² x – 4 ln x – 5| Evaluate - dx. e-3

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Q: m-1 Evaluate S²x²-1. [In (-²)]" dx 0

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Q: x2 dx = 17. x+1 18.The first step in calculating | dx is: (2x -4)(x+3)²

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

Q: I11 = +∞ -X e-* sin(2x) dx

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