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)+1) x d x is equal to
Options
- Ae^x 2 ( x- x )+c
- Be^ 2 x 5 (2 x- x)+c
- Ce ^ x 5 ( 2 x - 2 x )+ c
- Dnone of these
Correct answer
B. e^ 2 x 5 (2 x- 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