Search any question & find its solution
Question:
Answered & Verified by Expert
The value of $\int_{4}^{7} \frac{(11-x)^{2}}{x^{2}+(11-x)^{2}} d x$ is
Options:
Solution:
2004 Upvotes
Verified Answer
The correct answer is:
$3 / 2$
Let
$$
\begin{aligned}
I &=\int_{4}^{7} \frac{(11-x)^{2}}{x^{2}+(11-x)^{2}} d x \\
&=\int_{4}^{7} \frac{x^{2}}{(11-x)^{2}+x^{2}} d x
\end{aligned}
$$
On adding Eqs. (i) and (ii), we get
$$
2 I=\int_{4}^{7} 1 d x=[x]_{4}^{7}=3
$$
$$
\Rightarrow \quad I=\frac{3}{2}
$$
$$
\begin{aligned}
I &=\int_{4}^{7} \frac{(11-x)^{2}}{x^{2}+(11-x)^{2}} d x \\
&=\int_{4}^{7} \frac{x^{2}}{(11-x)^{2}+x^{2}} d x
\end{aligned}
$$
On adding Eqs. (i) and (ii), we get
$$
2 I=\int_{4}^{7} 1 d x=[x]_{4}^{7}=3
$$
$$
\Rightarrow \quad I=\frac{3}{2}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.