Let’s find the most general antiderivative<\/strong> of the constant function: 3\\sqrt{3}3\u200b<\/p>\n\n\n\n We’re given a constant function: f(x)=3f(x) = \\sqrt{3}f(x)=3\u200b<\/p>\n\n\n\n This function returns the same value (\u221a3) for every value of x. The goal is to find its antiderivative or indefinite integral<\/strong>.<\/p>\n\n\n\n The integral of a constant aaa with respect to xxx is: \u222ba\u2009dx=ax+C\\int a \\, dx = ax + C\u222badx=ax+C<\/p>\n\n\n\n where CCC is the constant of integration.<\/p>\n\n\n\n Apply the rule to our specific constant 3\\sqrt{3}3\u200b: \u222b3\u2009dx=3x+C\\int \\sqrt{3} \\, dx = \\sqrt{3}x + C\u222b3\u200bdx=3\u200bx+C<\/p>\n\n\n\n \u222b3\u2009dx=3x+C\\boxed{\\int \\sqrt{3} \\, dx = \\sqrt{3}x + C}\u222b3\u200bdx=3\u200bx+C\u200b<\/p>\n\n\n\n An antiderivative<\/strong> of a function is another function whose derivative gives the original function. In this case, we are asked to find the most general antiderivative of the constant 3\\sqrt{3}3\u200b.<\/p>\n\n\n\n The constant 3\\sqrt{3}3\u200b, which is approximately 1.732, is a real number and does not depend on the variable xxx. So when we integrate it with respect to xxx, we are essentially summing the constant value over a range of xxx values. That means we are looking for a function whose derivative is a constant.<\/p>\n\n\n\n The derivative of 3x\\sqrt{3}x3\u200bx is 3\\sqrt{3}3\u200b. Therefore, 3x\\sqrt{3}x3\u200bx is an antiderivative of 3\\sqrt{3}3\u200b. But to express the most general<\/strong> antiderivative, we must also include an arbitrary constant CCC, because the derivative of any constant is zero. Adding any constant to 3x\\sqrt{3}x3\u200bx will still result in a derivative of 3\\sqrt{3}3\u200b.<\/p>\n\n\n\n That is why the answer is: 3x+C\\sqrt{3}x + C3\u200bx+C<\/p>\n\n\n\n This formula captures all possible antiderivatives<\/strong> of the function f(x)=3f(x) = \\sqrt{3}f(x)=3\u200b. It includes every vertical shift of the line 3x\\sqrt{3}x3\u200bx, each of which has the same constant slope and thus the same derivative.<\/p>\n\n\n\n Including the constant CCC is important in indefinite integrals because differentiation loses constant information. Integration restores the family of functions that could have led to the same derivative.<\/p>\n\n\n\n So, the most general antiderivative of 3\\sqrt{3}3\u200b is: 3x+C\\boxed{\\sqrt{3}x + C}3\u200bx+C\u200b<\/p>\n\n\n\n Find the most general antiderivative : Square root of 3 Please with clear hand writing, will down vote if I cant understand the numbers and explanation. The Correct Answer and Explanation is: Let’s find the most general antiderivative of the constant function: 3\\sqrt{3}3\u200b Step 1: Understand the Function We’re given a constant function: f(x)=3f(x) = […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-34097","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34097","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=34097"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34097\/revisions"}],"predecessor-version":[{"id":34103,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34097\/revisions\/34103"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=34097"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=34097"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=34097"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nStep 1: Understand the Function<\/strong><\/h3>\n\n\n\n
\n\n\n\nStep 2: Use the Rule for Integrating a Constant<\/strong><\/h3>\n\n\n\n
\n\n\n\nStep 3: Apply the Rule<\/strong><\/h3>\n\n\n\n
\n\n\n\n\u2705 Final Answer:<\/strong><\/h3>\n\n\n\n
\n\n\n\nExplanation<\/strong><\/h3>\n\n\n\n
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<\/figure>\n","protected":false},"excerpt":{"rendered":"