1 [x²Pn (x)dx, n=0,1,2. -1 Q.3 Evaluate:

Q: ! 6-Find the value of the integral * U x3/2 e-x dx

A:

Q: Evaluate the integral dx (3x + 15)²’ by making the appropriate substitution: u = dx + 15)?

A: To evaluate:∫dx3x+152

Q: -1-y 3) Evaluate the integral dxdzdy?

A:

Q: 7. Evaluate the Integral S (x + 3) dx

A:

Q: 3. Evaluate the integral Sx cosx dx.

A: Please see the below picture for detailed solution.

Q: 4- 2x Evaluate the following integral : dx 2x +4,

A: The answer is π/3.

Q: 3. 'Evaluate the integral. 5 dx х0.2

A:

Q: 1 (b) Evaluate the integral S ; dx 2x2-12x+26

A: To evaluate: The integral of . Formula used: Integration Formula:

Q: In (T/e) ( (2- sec?x)eme sec³x sec (зА - х) -dx to be integrable using the formula и" du? ? What…

A:

Q: Evaluate the integral. dx a > 0 (a² + x²j3/2?

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: Prove that m-l dx =0 m +n (し+x)" where m,n are both Positive

A:

Q: Q6) Compute the integral 3 1 dxp -з (х +2)3

A: Here we solve the given integral.

Q: Derive a formula for In x dx where a. nt-1 b. n=-1

A:

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

A:

Q: (a) Evaluate the integral ſ x e2x çdx (2x+1)²

A:

Q: Evaluate the integral. HINT: 3 x2 dx J2 x - 1

A:

Q: 1.5 3-y Q1) Evaluate the integral dx dy

A: To evaluate the given integral.

Q: Prove that Jn (x) X good dx=1. n

A:

Q: 4х+2 Evaluate the integral -dx. (Hint: Use Algebra to help further rewrite your (x² +1)(x=1)…

A: First break by using partial fraction then integrate

Q: 2 1 The approximation of -dx by the composite Trapezoidal Rule with n=2 is O x+4 0.30833 0.40833…

A:

Q: (a) Evaluate the integral 1 2 (4-)dy dx

A: Evaluate the given integral as follows. ∫01∫024-y2 dy dx=∫01∫024-y2 dy dx=∫014y-y3302 dx=∫018-83…

Q: |1-y2 ху Q3. Evaluate the double integral dxdy /1– y²,

A: We have to find solutions

Q: 2e Evaluate the integral dx 2x +3

A:

Q: 4. Using the definition of sech x ,x 0 in terms of e , prove that 1+V1-x2 sech x = In ,0<x <1 Hence,…

A: 4) i)

Q: =Sin n dQ 2Q= 2. dt 10+2t

A: Given, a)y'+y=sinx b)dQdt+210+2tQ=4; Q(2)=100

Q: f(x) = In(2 + cos x). -2.125, xk+1 = Ik +0.5, yk = f (xk), k E N To = %3D %3D = 0r

A: The function is fx=ln2+cosx Conditions: x0=-2.125, xk+1=xk+0.5, yk=fxk, k∈ℕ xk+1=xk+0.5…

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

A:

Q: Compute dx using the techniques as presented in class and in our textbook. Show all 2x +5x-3 the…

A: we first factor the denominator

Q: - 3+ In x 3+ In x dy show that dx 2. (i) Given that y = [2] x(3 + In x)? 12 (ii) Hence evaluate dx .…

A: (i) Given : y=-3+ln(x)3+lnx Therefore, taking derivative both sides w.r.t x :…

Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: (2823 у — 3D 252*у — 6 sin 3а) dx (20x°y3 – 21a*y?) dy 4.4 - -

A:

Q: 57 Evaluate the integral |[xy dy dx. 12

A:

Q: d 1 Prove -[arctan r dx x² + 1

A: Given query is to find the derivative of arctan x.

Q: Evaluate the integral. 고-36 x² – 36 . 6cos- (승) +0 /x² – 36 - dx = Vx² – 36 – 6cos¬! + C x² – 36…

A:

Q: 1 . Evaluate the integral: S, S (4x³ + 6xy - 3y²) dx dy -1

A:

Q: if p> 1, (diverges; if p <1. 0o dx Prove that f p- 1 хР 1 Hence evaluate: dx. x6

A:

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: In(x) -dx Evaluate the integral m(2)

A:

Q: 2 Evaluate the improper integral 4x e dx, if exists. 8.

A: Given that,           ⇒           ∫-∞2e4x dx   ,   if exist             ⇒         find the…

Q: Q1. Evaluate the integral S dx (x + 1)(x² + 1)

A: We need to evaluate the following integral ∫01dxx+1x2+1

Q: -3 evaluate the integral (x2 – x + 2) dx using its definition.

A:

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

A:

Q: E valvate cox³ (x²+3)dx 2.

A:

Q: Evaluate the integral. B 4х- 3 dx J2

A: To evaluate:

Q: (b) Evaluate the integral | xe * dx. (1- x)?

A: Given : The integral is ∫ xe-x (1-x)2 dx .

Q: 2. S*3*+2 dx x+2

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: If u(x, y) = 2 tan-1 2 and v= In (x² + y?) , prove that: a2v = 0 дхду dx2

A:

Q: Q2: Evaluate the integral S Vx² – 2x + 1 · dx 3,

A: To Evaluate:

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.