A Simple Problem on Finding Integral of a Function

Integral of a Function is very easy to evaluate the value of function. Here is such Integration problem with multi choice answers.

Topic : Integral of a Function

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Problem : The function y(x) satisfying

Choice b is incorrect because of not adding the constant of anti-differentiation to the integral.

Choice c is incorrect because of committing the mistake to write the anti-derivative of 1 / (1 + y²) as cot^-1 y.

Choice d is incorrect because of failing to find the integral correctly.

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Question to Find Maximum Distance in the Elliptical Orbit

Topic : Ellipse

Question : Halley's comet has an elliptical orbit with the sun at one focus and a major axis of 1,636,484,848 miles. The closest the comet comes to the sun is 54,004,000miles. What is the maximum distance from the comet to the sun?

Solution :

2a = 1,636,484,848miles
so SC = 54,004,000miles
maximum distance from comet to the sun will be DS.
That is when comet comes at D
there is a maximum distance from sun
So SD = CD - SC ; CD = major axis = 1,636,484,848 miles
= 1,636,484,848 - 54004000
= 1582480848miles
So maximum distance is 1582480848miles.

Word Problem to Find Combinations of Tickets

Topic : Word problem

Question : The owner of a movie theater was counting money from1 days sales. he knew that the total of 150 tickets were sold. adult tickets cost 7.50 annd children tickets coast 4.7.5 each if the total recipt for the day were 891.25 how many of each kind of ticket was sold?

Solution :
Number of adult's ticket sold be 'x'
number of children ticket sold be 'y'

the total tickets are 150
So the first equation becomes x+y = 150 ------ (1)

cost of one adult's ticket be 7.50
cost of a child ticket be 4.75

total amount after selling all the tickets makes another equation
7.50x + 4.75y = 891.25 -------- (2)
________________
(x+y = 150) X 7.50
7.50x + 7.50y = 1125
7.50x + 4.75y = 891.25
- _____ -______-______
2.75y = 233.75
divide by 2.75
y = 233.75/2.75
y = 85
x + y = 150
x = 150 - y = 150 - 85 = 65

Problem to Find Unknown Angle of a Triangle

Topic : Angle of a Triangle

Solved Word Problem on Standard Deviation

Topic : Standard Deviation

Question : The average amount customers at a certain grocery store spend yearly is $636.55. Assume the variable is normally distributed. If the standard deviation is $89.46, find the probability that a randomly selected customer spends between $550.67 and $836.94.

Solution :

A Simple Integration Problem

Topic : Integration

Problem : Integrate x Cos x dx

Solution :

Order of Differential Equation with Example

Topic : Differential Equation
Question : State the Order of Differential Equation with Example.
Solution :
The order of the heighest order derivative occuring in a differential equation is called Order of the Differential Equation.
Example :
1) dy/dx +Cos x = 0
2) d²y/dx² = e^x