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

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Question

Evaluate the integral by using substitution.

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

Sum

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Solution

`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

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Chapter 7: Integrals - Exercise 7.10 [Page 340]

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NCERT Mathematics Part 1 and 2 [English] Class 12

Chapter 7 Integrals
Exercise 7.10 | Q 7 | Page 340

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