19-x² dx 2

Q: 9-x2 x dx

A: ∫9-x2x2dx=∫cot2udu=∫ -1+csc2udu=-∫ 1du+∫csc2udu=-u-cotuSubstitute back…

Q: 1 X-X -dx ах 3, -8 2vx

A:

Q: [x²√1-x² dx

A:

Q: •2 1 -dx- J-3 (x + 7)(x² + 16)

A: Given integral is Apply partial fractions to break the denominator

Q: | 2(x - 1)(x5 - 6x + 9)-5 dx

A:

Q: (x-1) 12-3x dx

A: It can be solved directly

Q: '3 | (x2 - 7) dx 1 4x +

A: Given: ∫13(x2-4x+7)dx To find: Evaluate the integral.

Q: 6. |x²e-2*dx

A: Solved below

Q: (2²–4)* -dx (x-2)²

A: We have to find the given integral

Q: 10. x3 Vx² –- 1 dx

A:

Q: 3. 9x -dx (x² +7)

A:

Q: 6. 1 -dx x3 4

A: We have to find integration and we have to substitute limits later.

Q: •5 b) 3 -dx x – 3

A:

Q: x + 3 -dx х — 1

A:

Q: 5 ,2 X |x² + x – 6| dx -5

A:

Q: Number 20

A: To evaluate

Q: ∫(x^3-4x)dx

A: The given integral is- I=∫x3-4xdx Then, ∫x3dx=x3+13+1=x44 & ∫4xdx=4x1+11+1=4x22

Q: Sx sech2 x² dx

A: Given:  Integral of xsech2x2

Q: x²(x³ - 2) dx

A:

Q: x4 – 4x3 + 8x² – 13x + 13 dx - - (x – 1)(x2 + 4)

A:

Q: 3-4x-10 x²-x-6 dx.

A: Given integral ∫x3-4x-10x2-x-6dx. The objective is to evaluate the integral.

Q: • 4 13х + 12 -dx x2 + 3x 3

A: ∫3413x+12x2+3x-4dxApplying completion of squares:=∫3413x+12x+322-254dxSubs u =…

Q: Solve s(4- dx 3x2

A:

Q: (x² + 4)³/2 -dx

A: Given integral is: I=∫x2+432xdx Integrating it: Put:u=x2+4dudx=xx2+4dx=x2+4xdu…

Q: 8 11xe-x dx

A:

Q: .3 - 16x + 6 dx x +4

A: Solution Given We need to find the integration

Q: Find 2 / 9-4x² 2 9-4x² dx. dx =

A:

Q: 2 x -dx 6. Jo 1-x

A:

Q: 1-3x dx Jo J2x-3x² 4. 2х— Зх?

A: Given problem is

Q: 1- (x².e2). dx

A: First integrate the function: ∫x2e2xdxIntegrate by parts: ∫fg' = fg-∫f'ghere f=x2, g'=e2xf' = 2x,g…

Q: 9. -1 2x xe dx

A: We have to find out solution of integral

Q: ¹₁¹+x² x + 2y dy dx -12x²

A:

Q: 4. √₁² √9-x² dx

A: Follow the procedure given below.

Q: 5 -dx 1+ x2

A:

Q: 2 19-x² 4 x² X dx

A: Solution of given question is written in below steps.

Q: x-2 x² - 4x-9 -dx

A:

Q: -4/3 – 2x – x² dx

A:

Q: 6 1-x² dx

A:

Q: x + 1 -xp- x + 3 x2 + 2x – 3 x2 3 dx ,

A:

Q: 4–9x² -dx

A:

Q: 1. 4x°dx (2-x*) ° 6

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 2x + 5 4. -dx x2 + 16

A: Given: Let I=∫2x+5x2+16 dx To Find: To evaluate the given integral.

Q: 25-9x2 -dx- x2

A:

Q: 7. sech²(Inx) dx X

A: Let's solve given integral.

Q: SV2*- 16 dx 2.x

A: Consider the integral: ∫e2x−16dxApply u…

Q: (13 -3x + 8 ) dx

A:

Q: 14- 2x (x-4) (x-1) dx =

A:

Q: 2 Find 11 csc (4x)dx 11 csc (4x)dx

A:

Q: 20. Find f2x/(5x-3)dx

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.