2. Show that Rij = e'i = e';

Q: cos 2t dt 2.

A: Given:             ∫-π3π31-cos 2t2 dt Take the constant out: ∫a·fx dx=a·∫fx dx…

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Q: 10. dr S f(æ) dx = Choose...

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Q: if x~unif. (0,2),find the U.b. of p(lx - mul>= 2)

A: Given X~Unif(0,2) Result: if X~unif(a,b) then  Mean=(a+b)/2 Variance=(b-a)2/12

Q: E. Prove the following: 四- Iz.l 1.

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Q: Evaluate: S, Vte-t² dt.

A:

Q: 1) z = e(4+j3) lIn(6230°)

A:

Q: -3t 10. s = cj e" + c2 e" cos 51 + cz e" sin 51 + 123 O Sm + 5 Su + 17 s - 123 s = 100 O Sm + 17 Su…

A:

Q: B: 3:Use Gamma & Beta properties to evaluate : f (In x) 3 dx

A:

Q: If e dy then y-

A: We will evaluate the following Integral.

Q: 7. Compute •+∞ COS X x¹ + x² + 1 -dx.

A:

Q: ) prove thaE cos ( x) dx =- T e x" + x2 +l 213

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Q: 6) Find (cor dy of

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Q: Show that S, (In x)? dx = e – 2

A: The detailed solution is as follows below:

Q: Find ſ In(x) dx

A:

Q: Find the length of the curve y = In(e - 1) – In(e + 1), In 2 sxsIn 3.

A:

Q: 8 2 1. Reverse order, then integrate Sr) dydx.

A: Given:    Intergral is given

Q: 3. How would you classify AG? A J G

A:

Q: Assuming x E Z. Prove

A: Given, x∈ℤ, To prove that                 2|(x2-6x+5) ⇒2|x

Q: Prove that coshz =log ztv= {Hint : cosh z =e} 2.

A: Use the hint and prove this.

Q: 13. - (In t ² )º t dt

A:

Q: In 8) * dx Integrate and evaluate the following

A: we have to integrate the following

Q: Find z when In z = e – nj

A: Complex number

Q: (22 – 2) | Evaluate dx 2+2 (x4+5x2 +4) tan1 2 A - BI E E E E X O Type here to search 马

A:

Q: az dz +y =5 ax If z= log ( x+x*y+y° ), Prove that x

A: We can prove this using the rules of partial derivative

Q: Is there a way to solve this w/o using L'Hospital's rule?

A: Solution

Q: Differentiate the following using the Chain Rule: 2. H( X)= ( 2X+4)³ 3. h(x)= (3x-4)? 4. x (x)= 2…

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Q: Compute Sinh Z c (az - z where C 121-1

A:

Q: What is R2 if beta = 0?

A: Solution : Consider a linear regression model, Yi = α + βXi + εi It is known that, coefficient of…

Q: 5. Evaluate the integral " Vtan o dex 1. de in terms of beta and Vtan gamma functions.

A:

Q: - seyi + avīj + () dt = 3 3

A: We have to perform integration by parts and then insert given limit

Q: 21. |'t cosh t dt Jo

A: Note:- These are multiple question and according to our company guideline we can do maximum one…

Q: 5. Express the integral: e- dr in terms of gamma function.

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Q: 3. ncnt) use PMI to prove that E

A:

Q: Find (1,0) where y2 + x2 + eV = 0

A: Given y2+x2+ey=0 ⇒y2+ey=-x2⇒ddx(y2+ey)=-ddx(x2)⇒2ydydx+eydydx=-2x⇒dydx(2y+ey)=-2x⇒dydx=-2x2y+ey

Q: 27 e integral dx be transformed into one of

A: By using a trigonometric substitution x=3secθ where, 0≤θ≤π2. The integral ∫27x3x2-9dx can be…

Q: Compute L[ t et ] х.

A: Laplace Transforms: The Laplace transform of the function tkf(t) is given by, The Laplace Transform…

Q: 4 In(t) dt

A:

Q: In GL(2, Z,,). det

A:

Q: 3. Calculate S x²sin(x³ + 1)dx.

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Q: 12- show that x² J.(x)dx = x²J1(x) + x J,(x) – lo(x)dx

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Q: If you are trying to solve f et dx and you let u = e then: dv = du = v = vdu Write down the uv –…

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Q: Show that S ťe dt = 3VI

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Q: 4. Prove that ах x" ea" dx xn- п-1 ‚ax dx а а

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Q: Find Z in (1-j5) 2= tanh cos lat5 express in lagarithm Form

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Q: асe of A is

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Q: 1) cos(s*)dtds

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 4. Express the integral e-t tổ dt in terms of gamma function.

A: