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MermaidWonders
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True or False: Let $F(x)$ be an antiderivative of a function $f(x)$. Then, $F(2x)$ is an antiderivative of the function $f(2x)$.
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MermaidWonders said:OK... Here's what I came up with... took me a while but I'm still kinda confused with myself. :(
Let $u = 2x$. Then $du/dx = 2$ --> $dx = du/2$.
$\int f(2x)dx$ then becomes $\int f(u)(du/2) = (1/2)f(u)du = (1/2)F(u) = (1/2)F(2x)$.
Integral calculus is a branch of mathematics that deals with calculating the area under a curve. It involves finding the antiderivative of a function and using that to determine the area between the curve and the x-axis.
True or false questions in integral calculus are used to test a student's understanding of the concepts and principles of the subject. They help to reinforce knowledge and identify areas that need further study.
To determine if an integral calculus question is true or false, you must first understand the concept being tested. Then, you can either solve the problem using the appropriate techniques or use your knowledge of the concept to determine if the statement is true or false.
Yes, some tips for answering true or false integral calculus questions include carefully reading the question and identifying key terms, using your knowledge of the concepts and principles, and checking your work for any errors.
No, true or false integral calculus questions can only have one correct answer. The purpose of these questions is to test your understanding of a specific concept or statement, so there can only be one true or false answer.