Home
Class 12
MATHS
If A is a square matrix and e^(A) =I +A ...

If A is a square matrix and `e^(A) =I +A +(A^(2))/(2!)+(A^(3))/(3!)+....oo=(1)/(2){:[(f(x),g(x)),(g(x),f(x)):}]" where "A={:[(x,x),(x,x):}] and 0lt xlt 1, I` is an Identity matrix. `int (g(x)+1) sin xdx=`

A

`(e^(x))/(2) ( sin x-cos x)+c`

B

`(e^(2x))/(5) (2 sin x - cos x)+c`

C

`(e^(x))/(5) ( sin 2x- cos 2x)+c`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • METHOD OF SUBSTITUTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos

  • METHOD OF SUBSTITUTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Matrix Match Type)|2 Videos

  • MEASURMENT OF TRIGONOMETRICAL ANGLES

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (Assertion -Reason Type)|2 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise WBJEE 2026|23 Videos

Similar Questions

Explore conceptually related problems

If e^(A) is defined as e^(A)=I+A+A^(2)/(2!)+A^(3)/(3!)+...=1/2 [(f(x),g(x)),(g(x),f(x))] , where A=[(x,x),(x,x)], 0 lt x lt 1 and I is identity matrix, then find the functions f(x) and g(x).

If f(x)={(x^2+2,,,xge2),(1-x ,,,xlt2):} ; g(x)={(2x,,,xgt1),(3-x ,,,xle1):} then the value of lim_(x->1) f(g(x)) is

If g (x) is the inverse of f (x) and f(x)=(1)/(1+x^(3)) , then find g(x) .

f(x)={(x-1, -1lexlt0),(x^2, 0ltxle1):} and g(x)=sin x. Then find h(x)=f(|g(x)|)+|f(g(x))|

If f(x)={(1-|x| ,, |x|lt=1),(0 ,, |x|>1):} and g(x)=f(x-1)+f(x+1), then find the value of int_(-3)^5g(x)dx .

Let g(x)=2f(x/2)+f(x) and f''(x)lt0 " in "0lexle1 , then g(x)

'If int_(1)^(2)f(x)dx=int_(1)^(2)g(x)dx , then f(x)=g(x) ''. Examine the validity of the statement with examples.

If g(x) is the inverse of f(x) an d f'(x) =(1)/(1+x^(3)) , show that g'(x) =1+[g(x)]^(3) .