{"@context":"https://schema.org/","@type":"Quiz","dateCreated":"2026-05-07T10:47:20.036Z","dateModified":"2026-05-07T10:47:20.036Z","typicalAgeRange":"11-18","educationalLevel":"AP ECET Ceramic Tech","assesses":"Mathematics - integral","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalTopic","targetName":"integral"},{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"Mathematics"},{"@type":"AlignmentObject","alignmentType":"educationalExam","targetName":"AP ECET Ceramic Tech"}],"name":"Quiz about integral","about":{"@type":"Thing","name":"Mathematics - integral"},"hasPart":[{"@type":"Question","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","educationalLevel":"intermediate","name":"Question About integral","text":"$$\n\\int \\frac{dx}{\\sqrt{16-25x^2}}=\n$$}","encodingFormat":"text/markdown","comment":{"@type":"Comment","text":"Convert \$\\sqrt{16-25x^2}\$ into \$\\sqrt{4^2-(5x)^2}\$, then use the inverse sine formula."},"suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/markdown","text":"

\$\\frac{1}{5}\\sin^{-1}\\left(\\frac{5x}{4}\\right)+c\$

","comment":{"@type":"Comment","text":"\"\""}},{"@type":"Answer","position":1,"encodingFormat":"text/markdown","text":"

\$\\sin^{-1}\\left(\\frac{5x}{4}\\right)+c\$

","comment":{"@type":"Comment","text":"\"\""}},{"@type":"Answer","position":2,"encodingFormat":"text/markdown","text":"

\$\\frac{1}{5}\\sin^{-1}\\left(\\frac{x}{4}\\right)+c\$

","comment":{"@type":"Comment","text":"\"\""}},{"@type":"Answer","position":3,"encodingFormat":"text/markdown","text":"

\$\\frac{1}{5}\\sin^{-1}\\left(\\frac{4x}{5}\\right)+c\$\n\n

","comment":{"@type":"Comment","text":"\"\""}}],"acceptedAnswer":{"@type":"Answer","position":0,"encodingFormat":"text/markdown","text":"

\$\\frac{1}{5}\\sin^{-1}\\left(\\frac{5x}{4}\\right)+c\$

","comment":{"@type":"Comment","text":"Convert \$\\sqrt{16-25x^2}\$ into \$\\sqrt{4^2-(5x)^2}\$, then use the inverse sine formula."},"answerExplanation":{"@type":"comment","text":""}}}]}

\[ \int \frac{dx}{\sqrt{16-25x^2}}= \]

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The Correct Option is A

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