Question

The value of integral ${\int }_{\frac{1}{\pi }}^{\frac{2}{\pi }}\frac{sin\left(\frac{1}{x}\right)}{x^2}dx=$

• A. 2
• B. -1
• C. \N
• D. 1

Answer 1

The correct option is D 1

$Putt=\frac{1}{x}\Rightarrow dt=-\frac{1}{x^2}dxast=\frac{\pi }{2}and\pi \therefore {\int }_{\frac{1}{\pi }}^{\frac{2}{\pi }}\frac{sin\left(\frac{1}{x}\right)}{x^2}=-{\int }_{\frac{\pi }{2}}^{\pi }sintdt=-[cost{]}_{\frac{\pi }{2}}^{\pi }=-[cos\pi -cos\left(\frac{\pi }{2}\right)]=1$