Q4 a) 0, if x < 0 Evaluate Fourier integral representation of f(x) = ²/2, if x = 0 le-x, if x > 0 1,0 < x < 1 x ≥ 1 b) Evaluate Fourier sine transform of f(x) = {¹,0

Q: Integrate the following. 2. S

A:

Q: 4 x+4 dx

A: We have to evaluate ∫4x+4 dx.

Q: 86. e* dx et3

A:

Q: L{ - 2)н( — 3)}

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: 4.2 Find the value of *d(\rf°).

A: Solution: ∫02x5d|x|3 Now Let, |x|3=t Since for integration, limit given to us is from 0 to 2, which…

Q: show that 3. 2. 5/-

A:

Q: 5. x' = 1 1 6 161 611 X

A: Given : x'=116161611x To find : The solution of the given differential equation . We solve by…

Q: dx x? V4+x?

A:

Q: 3 4 dx . (5+2x)' 3. Evaluate

A:

Q: S= Fbin

A:

Q: S sec ydy

A:

Q: ハメー X1 YxJ dx |

A: Find the integral

Q: 4x Ite

A: ∫1+e4xe2xdx

Q: S5x sec?x dx 5.

A:

Q: 25. х* dx dy

A:

Q: From z = o =1.57

A:

Q: Let V, W, X, and Y denote the payoffs for the certificate of deposit, office complex, land…

A: Hello there! there are more than three sub parts in the question. according to our policies cannot…

Q: 59. ella xp-

A:

Q: Sor's Evaluate e" 2e* 5e dx

A: The given integral is ∫ex2ex5ex dx

Q: 6. 22x+x dx 5. f 22x

A:

Q: 8 3 Evaluate S -dx. 10 9x 4

A:

Q: In(12 x- 11) dx

A:

Q: dx Evaluate • (1–2x)² 0 1 1 2 O-1 o 1 2

A: We have ∫-∞0dx(1-2x)2

Q: 9. dx

A: One of the two main parts of calculus which are concerned with the study of integrals, as opposed to…

Q: 8 1.3 --√x dx

A:

Q: 1 46* dx

A:

Q: xx x dx

A:

Q: S Sec ta

A: Solution is below

Q: 2. Unit conversions: What is average natural erosion rate in millimeters per year? (1 meter = 1000…

A: Here the given unit of average natural erosion rate is in meter per year , we want to find average…

Q: 25n n"

A:

Q: 7. GU

A:

Q: If a ib and b i y, then b y

A: Given, Lines a, b, x, y  and  z a∥b b⊥y The, we have to find the correct option.