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  • Explain solution RD Sharma class 12 chapter 19 Definite Integrals exercise Very short answer type question 20 maths

Explain solution RD Sharma class 12 chapter 19 Definite Integrals exercise Very short answer type question 20 maths

Answers (1)

Answer: \frac{b-a}{2}

Hint: you must know the rule of integration for function of x


Given: \int_{a}^{b} \frac{f(x)}{f(x)+f(a+b-x)} d x

Solution:  \mathrm{I}=\int_{a}^{b} \frac{f(x)}{f(x)+f(a+b-x)} d x            ...............(i)

Using property \int_{a}^{b} f(x)=\int_{a}^{b} f(a+b-x) d x

 

\mathrm{I}=\int_{a}^{b} \frac{f(a+b-x)}{f(a+b-x)+f(a+b-(a+b-x))} d x

\mathrm{I}=\int_{a}^{b} \frac{f(a+b-x)}{f(a+b-x)+f(x)} d x        ................(ii)

Add (i) and (ii)

\begin{aligned} &2 I=\int_{a}^{b} \frac{f(x)+f(a+b-x)}{f(x)+f(a+b-x)} d x \\\\ &2 I=\int_{a}^{b} 1 . d x \end{aligned}

\begin{aligned} &2 \mathrm{l}=[x]_{a}^{b} \\\\ &2 \mathrm{l}=\mathrm{b}-\mathrm{a} \\\\ &\mathrm{I}=\frac{b-a}{2} \end{aligned}

 

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