मराठी

Evaluate d∫0π2tan7xcot7x+tan7xdx

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प्रश्न

Evaluate `int_0^(pi/2) (tan^7x)/(cot^7x + tan^7x) "d"x`

बेरीज
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उत्तर

We have I = `int_0^(pi/2) (tan^7x)/(cot^7x + tan^7x) "d"x`  ....(1)

= `int_0^(pi/2) (tan^7(pi/2 - x))/(cot^7(pi/2 - x) + tan^7(pi/2 - x)) "d"x` ......By (p4)

= `int_0^(pi/2) (cot^7 (x) "d"x)/(cot^7x "d"x + tan^7x)`  .....(2)

Adding (1) and (2), we get

2I = `int_0^(pi/2) ((tan^7x + cot^7x)/(tan^7x + cot^7x))"d"x`

= `int_0^(pi/2) "d"x` which gives I = `pi/4`

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पाठ 7: Integrals - Solved Examples [पृष्ठ १५१]

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एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
पाठ 7 Integrals
Solved Examples | Q 10 | पृष्ठ १५१

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