dx 3. J 2(81+x*)³/ª

Q: d Using the Chain Rule Twice Calculate 1+ Vx2 + 1. dx

A: Given function is 1+x2+1

Q: 3. (a) Determine S 2xe3*dx by using integration by parts.

A:

Q: 8. Evaluate the integral. 2 2 (a) S(4x°. 3x + 2x)dx - 1 4 4+6u (b) S(ou)du Vu 1

A: Using rules of integration & formulae of integration.

Q: E) INTEGRAL : 9.) S(5t3 + 2t? – 5t – 50)dt 10.) S(3x2 + 2x + 500)dx

A:

Q: 1. S(7x³ + 4x²)dx e*dx 2. J itez* 1+e2x 3. S(V1 – cos x)dx

A: We will these indefinite integrals as

Q: Evaluate the double integral : (y³ – 12x) dx dy -

A:

Q: 3. Integration by parts a.j 18x ( x+ 4)»

A: Given

Q: 2dx J x (3(ln x)2 + 12 In x – 15)

A: The given integral can be evaluated using the factorization and substitution technique.

Q: 2dx J = (3(ln x)² + 12 In x – 15)i -

A:

Q: (b). Evaluate the integral 6x Vx +4 dx.

A: Part(b) Given

Q: 18 dx Integrate using trig. Substitution: S- x² V9– x²

A:

Q: dx + 3tx = t4 Int+1, dt 2. t2. %3D

A:

Q: 1 Evaluate the improper integral dx. (x – 3)3/2' 3 -

A:

Q: Using an appropriate substitution, 3 the integral S dx equals: /1-4 (х-1)2

A: Here we have to evaluate I=∫31-4(x-1)2dx

Q: Evaluate the integral 2 dx where fx) if -2 s xs 0 16-2 if 0xs3

A: Given function is The integral isThe integral can be written as: Plugging the function and applying…

Q: Evaluate the integral. dx 4 a > 0 (a² + x²)3/2?

A:

Q: Show for Re(z) > 1 -dx r(2) ((2). 1 er 0.

A:

Q: In x 2. Integrate -dx , (i) using the sub stitution u = Inx (ii) using integration by parts.

A: Integrate by substitutions and by parts

Q: 4x2 Calculate the integral: dx 3/2

A: I use trigonometric substitution to calculate this integral to see full solution please visit 2nd…

Q: 18x? Evaluate the integral: -dx V49 – x2 -

A:

Q: 2x dx by taking n = 4 1+ x Use trapezoidal Rule to evaluate

A: trapezoidal rule

Q: Evaluate the double integral 2. dy dx 3/x

A:

Q: 5. Find the integral 1 -dx x -5x +6

A:

Q: Q2 Integrate by parts: ex sin x dx

A: find ∫exsinxdx we know, ∫u.vdx=u∫vdx-∫dudx∫vdx now, apply this on equation I=∫exsinxdx…

Q: 7. What is the order, degree and linearity of: (dy + 3x dx, d°x = ey dx3 8. What is the order,…

A: Note: since you posted multiple questions. As per our guidelines we are supposed to solve one…

Q: 2. Use the substitution u = x² and then Integration by Parts to evaluate / x³e**dx.

A: Given: ∫x3ex2 dx We substitute u=x2, that implies du=2x dx. By using this substitution, ∫x3ex2…

Q: 3 Evaluate the integral |x V2x +1 dx ?

A: ∫x22x3+1dx We need to integrate the given function.

Q: Evaluate the Integral dx 4. S V1-e-2x

A:

Q: (b) Evaluate f 3æ“ In6x dx using integration by parts.

A:

Q: dx J x2-4x+5

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

Q: sin(2t + ) dt e21-3 4 7 4 4 64e 7

A:

Q: dz Find dz -3 and of z = x³ In(1 + xy). dy

A:

Q: 4 x2 Calculate the integral: dx V64 – x2

A: Consider the integral ∫4x264-x2dx Here, the objective is to find the indefinite integral using…

Q: -32e* – 140 -dx J e2x +9e* + 20

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: b) y = [ dx Integrate. 13 +5

A:

Q: 5. Evaluate the integral. 1 -dx æ² – 1 a) b) S. +4 -dx x² + 4

A:

Q: Integrate تلد ا - تم( فیگ S (a² – v²) * 22)* dv where " a" is constant

A:

Q: dx 62 + x² Integrate:

A:

Q: 2x dx by taking n = 4. 1+x Use trapezoidal Rule to evaluate

A: on solving this we get

Q: Integrate f dx using integration by parts. x+1

A: Please refer the attached image for complete solution.

Q: 2. Evaluate the integral: 2xe-**dx -0

A: topic - integration

Q: 3 x2 Calculate the integral: dx V5 + a?

A: Given,          ∫3x25+x2dx

Q: approximation of I = [" f(x)dx using composite Simpson's rule with n=4 is:

A: In this question, we evaluate the definite integral by using the composite Simpson's rule for n=4.

Q: Q.4 Using the method of substitution the integral fxer-3 dx

A:

Q: 4. Prove 1 < | V1+ a dx <2 0,

A:

Q: Q1/ Evaluate 1 dx Jo 1+x² using Simpson's 1/3 rule Simpson's 3/8 rule i- ii-

A: Simpson's rules are techniques of numerical integration. Both 1/3 and 3/8 rules are explained in the…

Q: Evaluate the integral. 9. dx J2 (x² – 1)3/2

A:

Q: 2. Solve the ODE using Separation of Variables. dy dx 5x²+4 y+1

A:

Q: 19. Use integration tables to find J(6x +7)*/(6x +7)² +16 dx

A:

Q: Q1-Evaluate the integral 2х — 5 dx - х2 — 5х + 1 3

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

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.