D H said:The book is right.
A simple indefinite integral is an integral that does not have any limits or boundaries. It is also known as an antiderivative, and it is the inverse operation of differentiation. It is represented by the symbol ∫ and is used to find the original function from its derivative.
To solve a simple indefinite integral, you need to find the antiderivative of the given function. This is done by using a set of rules and formulas, such as the power rule, product rule, and chain rule. Once the antiderivative is found, you can add a constant of integration to get the final solution.
Yes, a simple indefinite integral can have more than one solution. This is because the constant of integration can take on any value, and each value will result in a different solution. However, all of these solutions will be equivalent to each other.
The purpose of a simple indefinite integral is to find the original function from its derivative. It is also used to evaluate the area under a curve, which has many practical applications in fields such as physics, engineering, and economics.
Yes, there are limitations to using simple indefinite integrals. They can only be used to find the antiderivative of continuous functions. Additionally, some functions do not have a closed-form antiderivative, making it impossible to solve using simple indefinite integrals.