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Evaluate the integral by using substitution. ∫01xx2+1dx

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Question

Evaluate the integral by using substitution.

`int_0^1 x/(x^2 +1)`dx

Sum

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Solution

Let `int_0^1 x/(x^2 + 1) dx`

Put x² + 1 = t

2x dx = dt

When x =1, t = 2; x = 0, t = 1

`therefore I = int_1^2 dt/t`

∴ `I = 1/2 int_1^2 dt/t = [1/2 log t]_1^2`

`= 1/2 [log 2 - log 1]`

`= 1/2 log 2`

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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 1 | Page 340

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