{"@context":"https://schema.org/","@type":"Quiz","dateCreated":"2026-05-07T11:32:01.896Z","dateModified":"2026-05-07T11:32:01.896Z","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":"$$\\displaystyle \\int \\sin^2x\\,dx=$$}","encodingFormat":"text/markdown","comment":{"@type":"Comment","text":"Use the identity \$\\sin^2x=\\frac{1-\\cos2x}{2}\$ before integrating."},"suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/markdown","text":"

\$\\frac{x}{2}+\\frac{\\sin2x}{4}+c\$

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

\$\\frac{x}{2}-\\frac{\\cos2x}{4}+c\$

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

\$\\frac{x}{2}+\\frac{\\cos2x}{4}+c\$

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

\$\\frac{x}{2}-\\frac{\\sin2x}{4}+c\$\n\n

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

\$\\frac{x}{2}-\\frac{\\sin2x}{4}+c\$\n\n

","comment":{"@type":"Comment","text":"Use the identity \$\\sin^2x=\\frac{1-\\cos2x}{2}\$ before integrating."},"answerExplanation":{"@type":"comment","text":""}}}]}

\(\displaystyle \int \sin^2x\,dx=\)

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The Correct Option is D

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