For z > 0, 옮(1 In (t³ + 1) dt A) In (x³ + 1) B) In (8z³ + 1) c) 2 In (z³ + 1) 2 In (z² + 1) D) 2 In (8z³ + 1) E) 24z? In (8z³ +1)

Q: (In x)* Integrate: 1

A: Given,            ∫1eln x4xdx

Q: is intea rable Primitive aR 2 > X 3 1 2. 1 ラメラ 。 (今さ うx 31 ラ× %3D >入う。

A: we have Fx=0            0≤x<12x-1    1≤x≤2and fx=1     0≤x≤12    1≤x≤2 i The primitive of a…

Q: Use the substitution formula to evaluate the integral. 2t dt -1

A:

Q: Prove that cosh-z = In (z + vz? - 1) %3D

A:

Q: Evaluate the integral. 4 (5 - t)Vt dt

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

Q: Evaluate the integral dx 2VX3 - 3x Vx 1 V3x - V2 +C In 2/2 /2 + V3x In 1 +C 2/2 2 - V3 O In(2 V x3 -…

A:

Q: -25 Evaluate the integral: dax x²Vx2 +25

A:

Q: 3dz 1. S 4-5z

A:

Q: Find the simplest integrating factor u(x) of - xy' = (8x + 9)y + x In(x). µ(x) = %3D

A: As the given equation is an first order differential equation ,we can find integrating factor.

Q: Find of z = In(xy)

A: Given,Z=ln(xy)differentiating both the sides partially w.r.t. x∂z∂x=1xyy1∂z∂x=1xagain differntiating…

Q: Evaluate the integral dydx 3. 1-X 2

A: Use polar coordinates for simplification of the given integral.

Q: 12 Integrate: ,V4 - z² + dr

A: The given function is 4-x2+x7+24-x2 We have to integrate this function over the interval -2, 2

Q: Evaluate fz² In z dz using integration by parts 2 Onz-+ +c Oz-+ Onz-+c Oz² Inz - 2 + c

A: ∫z2lnzdz=∫(lnz)z2dz=(lnz)z33-∫1zz33dz+c=(lnz)z33-∫z23dz+c=(lnz)z33-13z33+c=(lnz)z33-z39+c=z33(lnz)-z…

Q: Prove that Cosh [m(t-x) Cosh mh 2mL 2mL

A: The given data is: To prove: emx1+e2mL+e-mx1+e-2mL=coshmL-xcoshmL

Q: calculate the 4-) integrals rdr a-) b-) (x2-9r+20)dr (-3)a

A:

Q: Find the local linear approximation of f(x) = In(5 + x) at xo = -4. %3D In(5 + x)

A:

Q: Evaluate the integral (2a+4)(x² + 4x + 2)*dx 4 by making the substitution u = x+ 4x + 2. ,2

A: Let u=x2+4x+2, now differentiate it with respect to x. du = (2x+4)dx So,…

Q: y = sech*x = In(_+ V1- x², sechx = In(- 1+ V1-x² Prove that .... ..

A:

Q: Evaluate the iterated integral: dydx - 1/4 Jx2

A:

Q: Evaluate the integral of * xdx Vx2-6х +13 |x-3+ (x-3)- 3 In Scx – 3)² – 4 + c x-3 3 In 6x +13 Option…

A: Explained below

Q: Explain Bessel equation and Prove that 2 (n + 4)Jn+4x (i) (ii) In+3X + Jn+5X = 4J"n = Jn-2 – 2Jn +…

A: The objective is to explain Bessel equation and prove that  (i) Jn+3x+Jn+5x=2xn+4Jn+4x (ii)…

Q: Prove using the IVT. ex + In x = 0 has a solution.

A: IVT: If f is continuous on the closed interval [a, b], f(a) ≠ f(b) and k is any number between f(a)…

Q: Evaluate the integral " -2n 1+4cost dt. 17-8cost

A:

Q: 4. Evaluate the integtral. (1) S dt 3

A: To evaluate the given integral we will use the following rule of integration: Now we have:

Q: ar integral of the c 3 – 7D2 + 7D – 2

A:

Q: Evaluate the integral dx 2x리x-3월 x2 1 3 + V2x In A + C 2/3"3 - V2 | ® In(2x x - 3{x²) +c 1 In + C…

A:

Q: Consider the integral 2 6z² In(z) dz

A:

Q: find the product of the integral 1- Sn) xy evx² dydx

A: To evaluate the double integral, first find the integral ∫0ln7yex2ydy. Consider the substitution…

Q: Evaluate the integral. 2 Ỉ -1 7t sec ¯¹t dt 2/√√3 2 7t sec¹t dt =

A:

Q: Prove that, cosh-'x = In |x + vx² – 1 for x 2 1 -기/

A: This question is based on Cosine hyperbola.

Q: Evaluate the integral. V36 – x² dx = 18sin- +xV36 – x² + c V36 – x² dx = 36sin--xV36 – x² + C / V36…

A:

Q: compute J secx dr. I n trying to integrate

A:

Q: A square is expanding in such a way that its diagonal is increasing at the rate of 2 in/s. (a) At…

A: GIven,  a square is expanding in such a way that its diagonal is increasing             at the rate…

Q: I need help understanding/ solving attached question for CALC.

A: Given the two parametric form of the line segment from (3,0,1) to (1,4, -2).

Q: Evaluate the integral fff, xyzdV,where: E = {(x, y, z)|–1 <x< 1,0< ys 2,1 szs 2}

A:

Q: Consider f dr. V1-16z² For the u-substitution u = 1 – 16x², which is the new integra 32 u2

A:

Q: How do you integrate z/(z+2) in terms of z?

A: Here, integral is,

Q: 1 Integrate 1+25cosx

A: To evaluate: ∫11+25cosxdx Let, I=∫11+25cosxdx Since, we know that cosx= 1-tan2x21+tan2x2…

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: 1. What should be A for the path independent of (2,4) xy + A 2Ay – x + xp- y? fip- (1,2) Moreover…

A: According to the given information, it is required to find the value of  so that the below integral…

Q: dr 4 – z Integrate:

A: The given integral,∫54-x2dx

Q: Show that {zn}nEN is Cauchy, where z, = sint dt. 1+t

A: Sol

Q: Evaluate the integrals

A:

Q: Evaluate the integral. 0. LG + dt - -2

A: final answer is -5.619 detailed solution is given below

Q: Find the integral. [(3 - 7x° + 5) dx 7 OA. 9x° -**5 7x* +5x +C O B. °-** 7 + 5x +C OB. Oc. 9x°. -**…

A: According to the properties of integration we have: ∫[f(x)±g(x)] dx=∫f(x) dx ± ∫g(x) dx

Q: Evaluate the integral. 3. [(ax-2-4) dx 2.

A: The given integral,        ∫234x-2-4dx

Q: Evaluate the integral dx 2x3 - 3x x |/3x - /2 2/2"V3x + v2 1 +C O 16V2 + V3 In 3 |/2 - 3x +C In +C…

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.