You might want to re-check your integral. What is:jimen113 said:Homework Statement
[tex]\int[/tex][tex]^{5}_{0}[/tex] 1+2x[tex]^{3}[/tex]
Homework Equations
answer is: 635/2
The Attempt at a Solution
Integrating the function I get this: 1/2(x+x[tex]^{}4[/tex])
Note that:jimen113 said:[tex]\int1[/tex]=x
[tex]\int 2x^3[/tex] = [tex]\frac{x^4}{2}[/tex],
1/2[tex]\int[/tex]x+x^4
I took (1/2) out of the [tex]\frac{X^{4}}{2}[/tex]
(So, maybe I can't do that, I should leave it and evaluate at the limits using (x^4/2)?
Evaluating an integral means finding the value of the integral, which represents the signed area under the curve of a function over a given interval. It is a fundamental concept in calculus and is used to solve a variety of real-world problems.
To evaluate an integral, you can use various techniques such as the fundamental theorem of calculus, integration by substitution, or integration by parts. It is important to understand the properties and rules of integration in order to determine the correct method to use.
A definite integral has specific upper and lower limits of integration, while an indefinite integral does not. In other words, evaluating a definite integral gives a numerical value, whereas evaluating an indefinite integral gives a general antiderivative of the function.
Yes, some calculators have built-in integration functions that can evaluate certain types of integrals. However, it is important to understand the process of evaluating an integral by hand to ensure accurate results and to be able to apply the concept in various scenarios.
You can check your answer by taking the derivative of the function you integrated and seeing if it matches the original function. Another way is to use numerical methods such as the trapezoidal rule or Simpson's rule to approximate the integral and compare it to your answer.