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Evaluate the integral by using substitution. ∫-11dxx2+2x +5

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प्रश्न

Evaluate the integral by using substitution.

`int_(-1)^1 dx/(x^2 + 2x  + 5)`

योग
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उत्तर

`int_-1^1 dx/(x^2 + 2x + 5)`

`= int_-1^1  dx/(x^2 + 2x + 4 + 1)`

`int_-1^1 dx/((x + 2)^2 + (1)^2)`

`= 1/2 [tan^-1  ((x + 1)/2)]_-1^1`

`= 1/2 [tan^-1 (1) - tan^-1 0]`

`= 1/2 [pi/4 - 0]`

`= pi/8`

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Evaluation of Definite Integrals by Substitution
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
Q 7
अध्याय 7: Integrals - Exercise 7.10 [पृष्ठ ३४०]

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एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 7 Integrals
Exercise 7.10 | Q 7 | पृष्ठ ३४०

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