MathMaster logo

MathMaster

  1. Home
  2. general
  3. the concept of the integral arose from the need to calculate the area of a curved region for example calculating the area
Question

The concept of the integral arose from the need to calculate the area of a curved region. For example, calculating the area delimited by the region above the x-axis and below the graph of the function f(x) = x3 in a given limited interval is not such a simple task if we consider the knowledge acquired throughout basic education. But the definition of Definite Integral allows us to obtain this area precisely. Thus, given the function f(x) = x3, the area of the region below the graph of f, above the x-axis in the interval from 0 to 2 is equal to.

134

likes
672 views

Answer to a math question The concept of the integral arose from the need to calculate the area of a curved region. For example, calculating the area delimited by the region above the x-axis and below the graph of the function f(x) = x3 in a given limited interval is not such a simple task if we consider the knowledge acquired throughout basic education. But the definition of Definite Integral allows us to obtain this area precisely. Thus, given the function f(x) = x3, the area of the region below the graph of f, above the x-axis in the interval from 0 to 2 is equal to.

Expert avatar
Brice
4.8
113 Answers
1. \ \text{Evaluate the definite integral of the function:}
A = \int_{0}^{2} x^3 \, dx

2. \ \text{Find the antiderivative of} \ x^3:
\int x^3 \, dx = \frac{x^4}{4}

3. \ \text{Apply the limits of integration} \ (0 \ \text{to} \ 2):
A = \left[ \frac{x^4}{4} \right]_{0}^{2}

4. \ \text{Evaluate the antiderivative at the upper limit (2) and lower limit (0):}
A = \frac{2^4}{4} - \frac{0^4}{4}

5. \ \text{Simplify the expression:}
A = \frac{16}{4} - 0

6. \ \text{Finish the calculation:}
A = 4

\text{Therefore, the area is} \ 4

Frequently asked questions (FAQs)
What is the square root of 96?
+
Math question: What is the derivative of f(x) = 3x^4 - 2x^3 + 5x^2 + 7x - 9?
+
What is the value of a missing angle in a triangle if the other two angles are 45° and 90°?
+
New questions in Mathematics
Calculate to represent the function whose graph is a line that passes through the points (1,2) and (−3,4). What is your slope?
A pump with average discharge of 30L/second irrigate 100m wide and 100m length field area crop for 12 hours. What is an average depth of irrigation in mm unIt?
a ferry travels 1/6 of the distance between two ports in 3/7 hour. the ferry travels at a constant rate. at this rate, what fraction of the distance between the two ports can the ferry travel in one hour?
5 squirrels were found to have an average weight of 9.3 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight
The gross domestic product the gdp for the United States in 2017 was approximately $2.05x10^3. If you wrote this number in standard notation , it would be 205 followed by how many zeros
Revenue Maximization: A company sells products at a price of $50 per unit. The demand function is p = 100 - q, where p is the price and q is the quantity sold. How many units should they sell to maximize revenue?
Consider the relation R defined on the set of positive integers as (x,y) ∈ R if x divides y. Choose all the true statements. R is reflexive. R is symmetric. R is antisymmetric. R is transitive. R is a partial order. R is a total order. R is an equivalence relation.
*Question!!* *Victory saved 3,000 in first bank and 2,000 Naira in union bank PSC with interest rate of X% and Y% per annual respectively his total interest in one year is #640. If she has saved 2,000 naira with first bank and 3,000 naira in union bank for same period she would have made extra 20# as additional interest, then find the value of X and Y
In a normally distributed data set a mean of 31 where 95% of the data fall between 27.4 and 34.6, what would be the standard deviation of that data set?
A job takes 9 workers 92 hours to finish. How many hours would it take 5 workers to complete the same job?
Divide 22 by 5 solve it by array and an area model
how many arrangement can be made of 4 letters chosen from the 8 letters of the world ABBSOLUTE
TEST 123123+1236ttttt
Buffalo Company makes and sells shampoo. Each unit requires $1.40 labor costs, material costs per unit are $0.90 and other variable costs are $0.30. It sells shampoo for $4.45 to retailers. Fixed costs are $15,000. It sold 25,000 units in the current month. What is the Break-Even point in units? What is the Break-Even point in dollars? What is the contribution margin of Buffalo Company?
2x2
factor the polynomial completely over the set of complex numbers b(x)=x^4-2x^3-17x^2+4x+30
To get to a hotel on the hill you have to travel 6 km of uphill road and every kilometer there are 6 sharp curves. Each of the sharp curves is marked by three traffic signs. How many traffic signs are there on the stretch of road that leads to the arbergi?
7- A printing company found in its investigations that there were an average of 6 errors in 150-page prints. Based on this information, what is the probability of there being 48 errors in a 1200-page job?
solve R the following equation 4 x squared - 35 - 9 over x squared is equal to 0
Triangle ABC has AB=AC and angle BAC =X, with X being less than 60 degrees. Point D lies on AB such that CB = CD Point E lies on AC such that CE= DE Determine angle DEC in terms of X

You might be interested in