st","extracted_subject":"MATH","extracted_chapter":"DEFINITE INTEGRAL AND AREA UNDER CURVE","extracted_topic":"FUNDAMENTAL DEFINITE INTEGRATION, DEFINITE INTEGRATION BY SUBSTITUTION","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1702.png?top_left_x=0&top_left_y=1048&width=532&height=239&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e70425d76b7ab31cc36","slug":"value-of-int-_-a-b-x---a-3-b-xsup4sup-dx-is","content":"Value of \$\\int _ { a } ^ { b } ( x - a ) ^ { 3 }\$ (b – x)⁴ dx is","options":[{"_id":"68a382687f15af4716b731fb","text":"\$\\frac { 1 } { 280 }\$ (b – a)⁸","sequence":0,"isCorrect":true},{"_id":"68a382687f15af4716b731fc","text":"(b – a)⁸","sequence":1,"isCorrect":false},{"_id":"68a382687f15af4716b731fd","text":"\$\\frac { 1 } { 280 }\$ (b – a)⁹","sequence":2,"isCorrect":false},{"_id":"68a382687f15af4716b731fe","text":"None of these","sequence":3,"isCorrect":false}],"correct_answer":"$$\\frac { 1 } { 280 }$ (b – a)⁸","explanation":"use x = a cos²q + bsin²q\n\nŽ dx = 2(b – a)sinq. cosq dq\n\nŽ I = 2(b – a)⁸ \$\\int _ { 0 } ^ { \\pi / 2 } \\sin ^ { 7 } \\theta\$ . cos⁹q dq\n\n= \$\\frac { 1 } { 280 }\$(b – a)⁸","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:36.041Z","__v":0,"vector_store_id":"75e9a58d-9274-48e6-b77d-2a83d8e4b279","updated_at":"2024-08-30T21:49:36.041Z","isStarred":false},"params":{"questionSlug":"value-of-int-_-a-b-x---a-3-b-xsup4sup-dx-is"}}]}]]

Question: Value of \(\int _ { a } ^ { b } ( x - a ) ^ { 3 }\) (b – x)<sup>4</sup> dx is...

Solution