₀¹ x/x²+1dx - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.10
Evaluate the definite integrals in Exercises 198 to 205 using substitution.

Question : 198 of 271

Marks: +1, -0

\int\limits_{0}^{1} \frac{x}{x^2+1}dx

Solution:

Let

I=\int\limits_{0}^{1} \frac{x}{x^2+1}dx

Put

x^2 + 1 = t

\Rightarrow 2x dx = dt

; When

x = 0, t = 1

and when

x = 1, t = 2

\therefore I=\frac{1}{2}\int\limits_{0}^{1} \frac{dt}{t}=\left[\frac{1}{2}\log t\right]_{1}^{2}

=\frac{1}{2}\left[\log 2 - \log 1\right]=\frac{1}{2}\log 2

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