Which of the following is equal to 01 On On² On ³ On¹ TL TL ΣΣΣ i-1 j-1 k-1 TL n

Q: Complete integral of the equation z = px+ qy – 2pq is, (a) z = ax+ by – Vab (b) z = ax+by + Vab (c)…

A: Clairaut's form is given by z = px+qy+f(p,q) Its complete integral is given by z = ax+by+f(a,b)

Q: Let a>0 and b be a real number. Use integration to confirm the following identities. 00 a -ах e cos…

A: Since multiple questions are asked, answering first with all sub parts. ∫0∞e-axcosbxdx=aa2+b2

Q: 1 1.3 D² +36 {12 sin 6x}

A:

Q: If z = In(x – y) + tan(x + y), show that Z = Z, XX

A: We have to show that given expression.

Q: xsin tx -dx [Ans : Te¯ª"] -at 5. * (x² +a³)'

A: ∫-∞∞x sin txx2+a2dx To Find: Evaluate using Laplace Transform:

Q: 3. Suppose that m and n are distinct (i.e., m n) positive inte- gers. Use the FTC to show that |…

A: Answer

Q: Given R = n 4- cos ( 4 + express the limit as n o as a definite integral, that is provide a, b and…

A:

Q: Evaluate the following integrals: 2. Inx de sin 3x 3. dx 1-cos 3x 4. S 32* dx 5. S(e* + 1)°e*dx 6.…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: 29.Verify that W[xλ cos(μ ln x), xλ sin(μ ln x)] = μx2λ − 1.

A:

Q: let y = x. In x find y'

A: Use product rule  of differentiation.

Q: 4.82. Show that f/2 sin² z dz= f/² cos² z dz = π/4.

A: To show that, ∫0π2 sin2 z dz=∫0π2 cos2 z dz=π4.

Q: 8(x²-a²) = 2a (cos - cos 0') [8(x-a) + 6(x + a)], 8(0 - 0′) sin 0 = 8(0-0') sin 0¹

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

Q: Q3. Evaluate the following Integrals Stan? 0 sec? e de | cos 7x cos 2x dx 4sin3x dx 1+cosx Q4.…

A:

Q: 2. | а) Determine the value of the following limits: ax? а- I. ,2 x 1+x? 1+x II. 1+x 1+x b) Find the…

A: Here we will use formula of limit limx→0sinxx=1 And chain rule of differentiation  dfgxdx=f'gxdgxdx…

Q: 5. Evaluate each integral. SHOW WORK!!! 12a+12bx? dx V3ax+bx³ п/4 b. S*(1+ tan x)³ sec² x dx а. c.…

A: These problems are solved using the substitution

Q: Evaluate the iterated integral 3 1- -cos (2) 2 06 0 3 - 3 cos (4) O 12 sin (2) .6 S² S²S (²³) 0 xdz…

A:

Q: |3x e dx 1.

A:

Q: 10 S In(Sint) 8(t + 3)dt -1 :Select one а. -3 b. 1 C. 10 d. 0 е. 3

A:

Q: Compute the definite integral π/4 x² sin(2x) dx = Cπ/4 x² sin(2x) dx. Enter exact values only help…

A:

Q: 5. Express 0 lim E (5x2 – 9x +16)Ax;[ – 8,4] as a definite integral. L (5x – 9)dx b. l' (10x – 9)dx…

A: The given sum is lim∆→0 ∑k=1n5x2-9x+16∆x; -8, 4. The given limit can be expressed as the integral of…

Q: √(x + y + 2)ds, where C' is parmeterized by Find the value of integral r(t) = (5 cos(3t), 2√6…

A:

Q: 1 dx =? (I+2)(r+1)² Lütfen birini seçin: O a.ln|a + 2| – ln|x + 1| + O b.ln|r – 2| – In|¤ – 1| – z1…

A: Use partial fraction decomposition to solve the integral.

Q: 1.4 Determine the following integrals 1.4.1 J sin x 9 cos²x+16 1.4.2 2tlnt dt. -1 1.4.3 x² +1 1.4.4…

A:

Q: Q.-Redvce the homogene ous Fredholm integral equatim 1 askene) ult) dt where Sin hx.sinhlt-1) sinh1…

A: To Reduce the homogenous fredholm equation into a boundary equation  Consider the given integral…

Q: S 2 1-a Select one: O True O False e²e³dydx = - (₁ e²d²) (²* eºdy) (² dx 2

A: Given :∫01∫21-xexeydydx=∫01exdx∫21-xeydy

Q: 20. (a) Use term by term integration to show f, In(l+1).dr – 1 – + - +... (justify why term-by-term…

A: We apply term by term integration to find the given integration and using Euler's formula to deduce…

Q: 2 + 5 sede) ( *)) d. /2+5 sed*). 3x 3x 4. 2 + 5 sec e tan

A: 4). Given: I=∫e3x2+5sece3xtane3xdx   ...1   As we know that; ∫secxtanxdx=secx+C