MHT CET · Maths · Definite Integration
The value of \(\int_{4}^{7} \frac{(11-x)^{2}}{x^{2}+(11-x)^{2}} d x\) is
- A 1
- B \(1 / 2\)
- C \(3 / 2\)
- D 0
Answer & Solution
Correct Answer
(C) \(3 / 2\)
Step-by-step Solution
Detailed explanation
Let
\(I =\int_{4}^{7} \frac{(11-x)^{2}}{x^{2}+(11-x)^{2}} d x \)
\( =\int_{4}^{7} \frac{x^{2}}{(11-x)^{2}+x^{2}} d x\)
On adding Eqs. (i) and (ii), we get
\(
2 I=\int_{4}^{7} 1 d x=[x]_{4}^{7}=3
\)
\(
\Rightarrow \quad I=\frac{3}{2}
\)
\(I =\int_{4}^{7} \frac{(11-x)^{2}}{x^{2}+(11-x)^{2}} d x \)
\( =\int_{4}^{7} \frac{x^{2}}{(11-x)^{2}+x^{2}} d x\)
On adding Eqs. (i) and (ii), we get
\(
2 I=\int_{4}^{7} 1 d x=[x]_{4}^{7}=3
\)
\(
\Rightarrow \quad I=\frac{3}{2}
\)
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