Evaluating Integrals: ∫_(-4)^1[f(x)]dx = (-125)/6

  • MHB
  • Thread starter Noah1
  • Start date
  • Tags
    Integrals
In summary, the notation ∫_(-4)^1[f(x)]dx represents the definite integral of the function f(x) from the lower limit of -4 to the upper limit of 1, which is the area under the curve of the function between these limits. To evaluate this integral, you would find the anti-derivative of the function and substitute the limits into it. The value (-125)/6 represents the numerical value of the definite integral, which can be evaluated using a calculator but it is important to understand the steps involved. Evaluating integrals has many real-world applications, such as calculating area, distance, volume, and probabilities.
  • #1
Noah1
21
0
Can anyone tell me if this is correct?
\int
∫1 at top and -4 on bottom of symbol [1^3/3+3 1^2/2-(4 x 1)+C] - [〖-4〗^3/3+〖3x(-4)〗^2/2-(4 x-4)+C]
If f(x) = x^2+3x-4, then F(x) = x^3/3+3 x^2/2-4x+C
∫_(-4)^1[1^3/3+3 1^2/2-(4 x 1)+C] - [〖-4〗^3/3+〖3x(-4)〗^2/2-(4 x-4)+C]
[1/3+3/2-4+C] - [-64/3+24+16+C]
[11/6-4+C] - [64/3-40+C]
11/6-4+C +64/3-40-C
= 139/6-44
= 139/6-(-264)/6
= (-125)/6
 
Physics news on Phys.org
  • #2
Hi Noah. :D

It's correct. As with any definite integral, you may leave out the constant of integration (C).
 
  • #3
thank you
 

Related to Evaluating Integrals: ∫_(-4)^1[f(x)]dx = (-125)/6

1. What does the notation ∫_(-4)^1[f(x)]dx mean?

The notation ∫_(-4)^1[f(x)]dx represents the definite integral of the function f(x) from the lower limit of -4 to the upper limit of 1. In other words, it represents the area under the curve of the function f(x) between the x-values of -4 and 1.

2. How do you evaluate this integral?

To evaluate this integral, we would first need to find the anti-derivative of the function f(x). Once we have the anti-derivative, we can substitute the upper and lower limits into the anti-derivative and take the difference to find the value of the definite integral.

3. What does the value (-125)/6 represent in this integral?

The value (-125)/6 represents the numerical value of the definite integral evaluated between the limits of -4 and 1. In other words, it is the area under the curve of the function f(x) between the x-values of -4 and 1.

4. Can you use a calculator to evaluate this integral?

Yes, you can use a calculator to evaluate this integral. Many calculators have a built-in integral function that can be used to evaluate definite integrals like this one. However, it is important to understand the steps involved in evaluating an integral by hand in order to fully understand the concept.

5. What are some real-world applications of evaluating integrals?

Evaluating integrals has many real-world applications, including calculating the area under a curve in physics or engineering problems, finding the total distance traveled by an object, and determining the volume of an irregularly shaped object in mathematics and engineering. It is also commonly used in economics and statistics to calculate probabilities and expected values.

Similar threads

B Why is this definite integral a single number?
    • Calculus
Replies
20
Views
3K
MHB Calculating the Derivative of a Function Using the Chain Rule
    • Calculus
Replies
2
Views
1K
MHB What Is the Minimum Surface Area for a Cuboid Box with a Square Base?
    • Calculus
Replies
4
Views
1K
I Substitution in a definite integral
    • Calculus
Replies
6
Views
2K
I Integration of √(1-x^2) with x=sinθ: Check Correctness and Simplification
    • Calculus
Replies
12
Views
2K
MHB Evaluate the surface integral $\iint\limits_{\sum}f\cdot d\sigma$
    • Calculus
Replies
1
Views
2K
MHB Q1 Can you pass this 3 question AP calculus Quiz in 10 minutes
    • Calculus
Replies
3
Views
794
I Express the limit as a definite integral
    • Calculus
Replies
16
Views
3K
I The Euler-Lagrange equation and the Beltrami identity
    • Calculus
Replies
1
Views
1K
MHB Evaluating $f'(1)$ for $f(x)=7x-3+\ln(x)$
    • Calculus
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top