(-1)^ dx n= (2n+1)!

Q: Integrate sin^2(7x)-cos(x)

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Q: Integrate the square root of (1 - sin² x) dx.

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Q: Use integration by parts to verify the reduction formula.

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Q: Integrate: S tan (æ) sec³(x)dx

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Q: Find a curve through the point ( 1 , 5/6 ) whose length on the interval [ 1 , 2 ] is given by ∫ 1^2…

A: The length of the curve y=f(x) from x=a to x=b is L=∫ab1+dydx2dx Now , Length of a curve on the…

Q: A light is hung 6 meters above a straight horizontal path.  If a man 2 meters tall is walking toward…

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Q: 14. √ √2-√x dx

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Q: tion, what is the longest time within whic at the predator will have to spend more t

A: It is found that the time (in minutes) required by predator to find a prey is a random variable that…

Q: The sides of a square decrease in length at a rate of 1 m/s. At what rate is the area of the square…

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Q: Solve 4 sin 2x S1₁= 8 4 -1 -¹x³ + x²-x² +2 dx

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Q: 4. Shirogane, who is 175 cm tall, is walking at a rate of 3 meters per second towards a lamppost…

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Q: 2. Find a real root of 3x – logi0 x – 8 using the Successive Approximation method. Correct to four…

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: A bacteria culture starts with 4 bacteria and grows at a rate proportional to its size. After 2…

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Q: dx Tx-1 4

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Q: In( cosh(7x) + sinh(7x)) + In( cosh(7x) - sinh(7x) ) =

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Q: The integ ral csc(0.5) dx is equal to

A: Follow the procedure given below.

Q: find integral sqrt (1 - 4x 2 ) dx

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Q: (Use Simpson's Rule with n=4 to approximate 5x* dx

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Q: Describe a first step in integrating x10 – 2r4 + 10x² + 1 -dx. 3x3

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Q: Use Simpson's Rule with n = 4 to approximate 5x* dx.

A: The solution is given as

Q: Find upper and lower bounds for

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Q: Estimate x² dx using left endpoints for n = 4 approximating rectangles. 3 x² dx is approximately

A: The equation of the integral function is ∫03x2dx. The left endpoints is n=4.

Q: logtan nx(2+ 4 cos nx) 2

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Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A: Given: when the initial time t=0 amount of the cane sugar is 75 kg, and the time t=30 minutes amount…

Q: 3 dx V16-x²

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Q: 2. Solve 3shn-sinx-2= over the interval [0,27). 2 sın'x-sinx-|:0

A: The objective is to solve the above expression.

Q: Each side of a square is increasing at the rate of 8 cm/sec. At what rate is the area of the square…

A: Solution :let, side of square=xArea of square=Adxdt= 8 cm/secA= 36 sq. cmA=x2    Area of square=side…

Q: •2 5. Calculate | x In(3x)dx.

A: Given integral:

Q: solve \int (sin^(5)x)/(cos^(2)x)dx

A: We evaluate  \int (sin^(5)x)/(cos^(2)x)dx

Q: find integral  sqrt ( x2 - 9 )dx

A: Given: I=∫x2-9dx we know that ∫x2-a2dx=x2x2-a2-a22lnx+x2-a2+c                                ..1

Q: A balloon is rising straight up from a level field, at a constant rate of 0.4 m/ sec. Just when the…

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Q: A bacteria grows proportional to the square root of its current population. Starting at an initial…

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Q: Exercises to solve: 1. fx² In(x + 1) dx 2. (x2 + x – 2).cos4x. dx 3. Se-*sinxdx 4. S sinh2x.cosh5x…

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

Q: The first derivative of the power series 3x2 3x f(x) = 3 1! 3x3 3x4 325 %3D - 2! 3! 4! 5! • is

A: Formulae: 1. e-x = 1-x/1! +x2/2! - x3/3! +x4/4!- ....... 2. d/dx{ e-x} = - e-x   Answer: f'(x)= f(x)

Q: integrate x^4cotx^5 dx from 0.4 to 0.8

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Q: q² In(x³ + 1) dx

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Q: Find the intergral of (5-4x)/(√(12x-4x^2-8) ) dx

A: It is given that,               (5-4x)/12x-4x2-8dx     we have to integrate it.

Q: for dx

A: Given integration is : ∫exdx To find the value given integration by parts.

Q: cosh(In x) dx

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Q: A tubular metal 3.9 meters long leans against a vertical wall and the other foot of the metal is on…

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Q: 2. A ladder 20 meters long leans against a wall. If the bottom of the ladder is being pushed towards…

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Q: A pole that is 74 feet long is leaning against a brick wall. The bottom of the pole is getting…

A: This question is related to rate of change, we will solve it using given information.

Q: 6) A light is 20 meters above a straight horizontal path. If a man 1.65 meters tall is walking away…

A: Given: Height of light is 20 meter. Height of man is 1.65 meters. Rate with which man is walking is…

Q: Integrate completely

A: Given,             ∫2x+12x-53dx

Q: Use the composite Simpson's rule with step length h=0.5 to determine 1= [ (2x - - 3x2 + 4x – 1)dx,

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Q: A lighthouse is located on a small island 3 km away fromthe nearest point P on a straight shoreline…

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Q: Ssin(3x) sin(7x) dx

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Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.