Q. If $e^{A}$ is defined as $e^{A}=I+A+\frac{A^{2}}{2 !}+\ldots \ldots =\frac{1}{2}\begin{bmatrix} f\left(\right.x\left.\right) & g\left(\right.x\left.\right) \\ g\left(\right.x\left.\right) & f\left(\right.x\left.\right) \end{bmatrix}$ where $A=\begin{bmatrix} x & x \\ x & x \end{bmatrix}$ and $0 < x < 1$ I is an identity matrix. Then $\displaystyle \int _{0}^{1}\frac{g \left(\right. x \left.\right)}{f \left(\right. x \left.\right)}dx$ is equal to
NTA AbhyasNTA Abhyas 2022
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