Most Important Selected Qs for JEE AdvancedMathematicsMatrices
Paragraph: If e^A is defined as e^A=I+A+ A^2 2! + A^3 3! + . .= 1 2 [ array ll f(x) & g(x) g(x) & f(x) array ] where A= [ array ll x & x x & x array ] and 0 x 1 , I is an identify matrix Question: g(x) f(x) d x is equal to
Options
- A( e ^ x + e ^ - x )+ c
- B( e ^ x - e ^ - x )+ c
- C(e^ 2 x -1 )+c
- Dnone of these
Correct answer
A. ( e ^ x + e ^ - x )+ c
Step-by-step solution
Here, e^A= 1 2 [ array ll e^ 2 x +1 & e^ 2 x -1 e^ 2 x -1 & e^ 2 x +1 array ] So, f(x)=e^ 2 x +1 ; g(x)=e^ 2 x -1