Jalo said:Homework Statement
(ignore what's written, it isn't important for the problem)
I'm studying integrals and I came across this solved example. However I can't understand where the minus of the integral came from came from.
Homework Equations
The Attempt at a Solution
The primitive of a f^p * f ' function is f^(p+1) / (p+1) Therefore it should be ln^2(x-1)/2 and not -ln^2(x-1)/2
Thanks
Solving an integral problem allows us to find the area under a curve, which is useful in many applications such as calculating volumes, work, or displacement.
If the function being integrated is negative over the interval of integration, then the integral will have a negative value. In this case, a minus sign must be included in the solution.
No, the minus sign is an important part of the solution for an integral problem. Ignoring it will result in an incorrect answer.
One technique is to draw a graph of the function and determine if the area under the curve falls below the x-axis. Another technique is to check the limits of integration and see if the function changes signs within those limits.
Handling the minus sign correctly ensures that the solution is accurate and reflects the correct area under the curve. It also helps to avoid errors in further calculations or applications of the integral.