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पाठ्यक्रम

If eeeed∫3ex-5e-x4e6x+5e-xdx = ax + b log |4ex + 5e –x| + C, then ______.

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प्रश्न

If `int (3"e"^x - 5"e"^-x)/(4"e"6x + 5"e"^-x)"d"x` = ax + b log |4ex + 5e –x| + C, then ______.

विकल्प

  • a = `(-1)/8`, b = `7/8`

  • a = `1/8`, b = `7/8`

  • a = `(-1)/8`, b = `(-7)/8`

  • a = `1/8`, b = `(-7)/8`

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उत्तर

If `int (3"e"^x - 5"e"^-x)/(4"e"6x + 5"e"^-x)"d"x` = ax + b log |4ex + 5e –x| + C, then a = `(-1)/8`, b = `(-7)/8`.

Explanation:

`(3"e"^x - 5"e"^-x)/(4"e"^x + 5"e"^-x) = "a" + "b" ((4"e"^x - 5"e"^-x))/(4"e"^x + 5"e"^-x)`,

Giving 3ex – 5e –x = a(4ex + 5e–x) + b(4ex – 5e–x).

Comparing coefficients on both sides,

We get 3 = 4a + 4b and –5 = 5a – 5b.

This verifies a = `(-1)/8`, b = `7/8`.

shaalaa.com
Definite Integrals
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
Q 22
अध्याय 7: Integrals - Solved Examples [पृष्ठ १५९]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
अध्याय 7 Integrals
Solved Examples | Q 22 | पृष्ठ १५९

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