Evaluate using Special Integral Forms MCQ Quiz in मराठी - Objective Question with Answer for Evaluate using Special Integral Forms - मोफत PDF डाउनलोड करा

Concept

\(\rm \int e^x \left(f(x)+f'(x)\right)dx \) = e^x f(x) + c

Calculation:

Let, \(\rm I=\int e^x \left(\dfrac{1}{x}- \dfrac{1}{x^2}\right)dx \)

Let f(x) = \(\rm 1\over x\)

⇒ \(\rm f'(x) = - {1\over x^2}\)

∴ \(\rm I=\int e^x \left(\dfrac{1}{x}- \dfrac{1}{x^2}\right)dx \)= \(\rm \int e^x \left(f(x)+f'(x)\right)dx \)

= ex f(x) + c

= \(\rm e^x ({1\over x})\) ​​+ c

Hence, option (3) is correct.