मराठी

Evaluate the following: d∫dx16-9x2 - Mathematics

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प्रश्न

Evaluate the following:

`int ("d"x)/sqrt(16 - 9x^2)`

बेरीज
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उत्तर

Let I = `int ("d"x)/sqrt(16 - 9x^2)`

= `1/3 int ("d"x)/sqrt(16/9 - x^2)`

= `1/3 int ("d"x)/sqrt((4/3)^2 - x^2)`

= `1/3 sin^-1  x/(4/3) + "C"`  ....`[because int ("d"x)/sqrt("a"^2 - x^2) = sin^-1  x/"a" + "C"]`

∴ I = `1/3 sin^-1  (3x)/4 + "C"`

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पाठ 7: Integrals - Exercise [पृष्ठ १६४]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 7 Integrals
Exercise | Q 14 | पृष्ठ १६४

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