The value of int_{4}^{7} frac{(11-x)^{2}}{x^{ | vedclass

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(C) Let $I = \int_{4}^{7} \frac{(11-x)^{2}}{x^{2}+(11-x)^{2}} d x$  $(i)$ Using the property $\int_{a}^{b} f(x) d x = \int_{a}^{b} f(a+b-x) d x$,we ge

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$3/2$

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(C) Let $I = \int_{4}^{7} \frac{(11-x)^{2}}{x^{2}+(11-x)^{2}} d x$  $(i)$ Using the property $\int_{a}^{b} f(x) d x = \int_{a}^{b} f(a+b-x) d x$,we get: $I = \int_{4}^{7} \frac{(11-(11-x))^{2}}{(11-x)^{2}+(11-(11-x))^{2}} d x$ $I = \int_{4}^{7} \frac{x^{2}}{(11-x)^{2}+x^{2}} d x$ $(ii)$ Adding $(i)$ and $(ii)$: $2I = \int_{4}^{7} \frac{(11-x)^{2} + x^{2}}{x^{2}+(11-x)^{2}} d x$ $2I = \int_{4}^{7} 1 d x$ $2I = [x]_{4}^{7} = 7 - 4 = 3$ $I = \frac{3}{2}$

The value of $\int_{4}^{7} \frac{(11-x)^{2}}{x^{2}+(11-x)^{2}} d x$ is

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