5. (5 – x)² * 6 Show that if y=3-x then %3D 6. . (x-s) _ xp 1. dx. 3 Hence, find the value of , 2(5 – x)² -

Q: 2. Evaluate the integral 4 dx V2x-5 5/2

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Q: Find the length of the graph of y = (1/2) cosh 2xfrom x = 0 to x = ln 25.

A: Length of the graph y=f(x),a<x<b is given by L=∫ab1+dydx2dx Here,  y=12cosh 2x⇒dydx=122sinh…

Q: how do you find z sub alpha over 2 using table a-2

A: I am solving this question by taking an example Let us take α = 0.05 We need to find

Q: 2 S (x) + x³)dx = ? -1

A:

Q: a. Determine the marginal p.d.f.'s of X and Y. b. Are X and Y independent? c. Are the event (X 1/2}…

A: It is asked to find the marginal pdf's of X and Y. Marginal pdf of X. fx(x) = ∫0132y² dy=32∫01y²…

Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to estimate I = In(2 +3/x) -dx, 12…

A: To use the composite Sympsopns 1/3 rule with step length h=0.4.

Q: 4) Evaluate the definite integral: S, (6x² – 3x + 7)dx.

A:

Q: 5) Find the general antiderivatives for the following; х-1 dx x* +2х-3 -dx 6)

A:

Q: [2] Determine the values of n and h required to approximate | a In(x)dx to within 10-10. Use (a)…

A: Hello. Since your question has multiple parts, we will solve first question  for you. If you want…

Q: 2. The rate at which the total average of COVID cases is dz increasing at r = 10 tents and than if…

A: If 30 tents are built, the average number of COVID cases per tent will be 7 cases while the average…

Q: 5 2 +2 ) dx using Estimate I - n = 4 subintervals and (a) Left endpoints. (b) Right endnoints.

A: solution:-I=∫152x+2dx,     n=4f(x)=2x+2∆x=5-14=1(a) Left end pointI=∆xf(1)+f(2)+f(3)+f(4)…

Q: 12. Find the dicections at.which. the directronal.derivative af.f.(hg)..xSin xy.at.(,a).has.…

A:

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to -1 (-24 x² – 10x³ -…

A: Given integral is ∫-4-1 -x4 -10x3 -24x2 -4x+4 dx Take  fx = -x4 -10x3 -24x2 -4x+4

Q: 2 Find つえdy 2 こ( beny s)

A:

Q: 9. Let Y1, Y2,..., Yn constitute a random sample from the pdf given by f (v) = (0 – y) for 0 sy sO.…

A: Given: The sample probability distribution function of Y1,Y2,......Yn is: f(y)=2θ2θ-y  for  0≤y≤θ

Q: Let X be gamma-distributed, with Var(X)= 2E(X) and moment generating function M, (3/8)= 2. %3D…

A:

Q: How do i find e(x), var(x) and e(x^3) using the moment generating function

A: Let us define the random variable X with moment generating function Mx(t).The moment generating…

Q: If X is exponentially distributed with parameter λ and Y is uniformly distributed on the interval…

A: Given, X is exponentially distributed with parameter λ Y is uniformly distributed on the interval…

Q: Find * In(x² + 2x + 2) dx (x + 1)² In|1 + (x + 1)²| x +1 In|1 + (x + 1)2| x + 1 + 2tan-(x + 1) +c…

A: I am attaching image so that you understand each and every step.

Q: The approximation of 1 = cos(x+10) dx using composite Simpson's rule with n-3 is: 1.01259 3.25498

A: In this question, the concept of Integration is applied. Integration Integration is a method of…

Q: If the 2n RVs A, and B, are uncorrelated with zero mean and E(A²,) = E(B²,) = %3D o, show that the…

A:

Q: 1. Evaluate 5 S Sx (x + 3x)dydx

A: Given, ∫05∫0x x(x + 3x) dy dx=  ∫05∫0x (x2 + 3x2) dy dx=  ∫05 ∫0x (x2 + 3x2) dydx= ∫05 ∫0x 4x2 dydx

Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+3/x) -dx, 9• I = 1+x²

A: Given: I=∫26 ln(2+3x)1+x2dx

Q: 8. (a) Show that (b) Evaluato 1/3 3 √1+9x² -4x4 dx dx = ln(1 + √2).

A:

Q: х — 1 Q8: Find dx. Vx2 + 4x + 5 A -Vx2 + 4x + 5 – 3 ln (V x2 + 4x + 5)+C -1 В x2 + 4x + 5 – 3 sinh…

A: Option (B) is correct answer.

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y * logy x |

A:

Q: Determine the GINI Index of Country X whose Lorenz curve is f(x) =;x² +÷x*. If Country Z 3 has a…

A: The Lorenz curve  of country X is f(x)=12x2+12x4. The GINI index  of a certain country with Lorenz…

Q: The coefficient of correlation between X and Y is - and o = a, of = 4a, and %3D %3D ož = 114 where Z…

A: Given: Z=3X-4Y. The coefficient of correlation between X and Y is 13and σx2=a, σy2=4a,σz2=114

Q: 5. Evaluate by using beta function: | °(1 – r*)} dx.

A:

Q: 8 Ay 10- f(x) dx using Compute the following estimate of 8- the graph in the figure. 6- S(4) 4- 2-

A: The given graph is  To find ∫08fxdx using Simpson's Rule with n=4

Q: 18 2 6x dx using n = 2, 4, and 8 subintervals 2

A:

Q: 8x + 1 10. Evaluate the integral / dx. 4.x2 + 12x + 10 11 (a) In |4.x2 + 12x + 10|| tan-(2x + 3) + C…

A:

Q: 5. Consider the function f(x)=e*, calculate df/dx with finite difference using forward and central…

A: We can solve this using formula of central difference and

Q: S x2 +2x-10 (2x+4) + 1 JE + 4x +5) Consider dx = x² (x² + 4x + 5) (2x+4) + 1 dx- x² + 4x +5 dx ,…

A:

Q: ( If X₁, X2,..., Xn constitute a random sample of size n from a population given by 2(0 - x) for…

A:

Q: Suppose that you estimated (1) w B +B za +e and based on the results, rejected the hypothesis that…

A: Given three regression models as I  yi=β1+β2xi2+ei II  yi=γ1+γ2xi2+γ3zi+ψi III  xi2=δ1+δ2zi+νi

Q: 7. Evaluate the integral. Vx2 – 25 dx х3

A: First we will make a trigonometric substitution of x=5*sec θ then we will solve it and integrate it.…

Q: II z= ě Y x - Juv Find dz dv üs ing chein rule.

A:

Q: Š The minimum value of n required to approximate dx by composite Simpson's Rule with an error less…

A: Given integral is ∫02e−2xdx. We have to find the minimum value of n required to approximate…

Q: 19. f(x. y) In(1 - x - y) %3D

A: As per our company guidelines we are supposed to answer only the first question that you have…

Q: Find the net change in ve]locity over [1, 4] of an object with a(t) = 8t − t2 m/s2.

A:

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

A:

Q: 9. y = Arccot“ Vx 2 Arccot Vx А. Arccot x С. Vx(1+x) x' +x* Arccot x В. Arccot x Vx(1-x) D. - -…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3.Please resubmit the question and…

Q: 1. If X,, X2, .X, forms a random sample of size n from a population with pdf f(x; 8,8) = 0 for x>0…

A:

Q: 5. prove that d (-x) (+ x) = X dx dx d² dx² - x² +1

A:

Q: 2. The rate at which the total average of COVID cases is dx = 1 tent per day, given dt increasing at…

A: Given,  number of tents= 20 and average number of cases will be 5

Q: 12) a) Use either the Trapezoid OR Midpoint Rule to estimate [ In(1+e* ) dx using at least four…

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

Q: 2x²-3x + 10 dx (x²+4)2

A: The objective of the question is evaluate the indefinite integral.