AP EAMCET202315 May 2023Morning ShiftMathematicsIndefinite IntegrationActual
Assertion (A): _ 6 ^ 3 ( x)^ 2 d x ( x)^ 2 +( x)^ 2 = 12 Reason (R): _ 6 ^ 3 f(x) d x f(x)+f ( 2 -x ) = 12
Options
- AA is true, R is true and R is the correct explanation of A
- BA is true, R is true but R is not the correct explanation of A
- CA is true, R is false
- DA is false, R is true
Correct answer
A. A is true, R is true and R is the correct explanation of A
Step-by-step solution
Let _ / 6 ^ / 3 ( x)^ 2 d x ( x)^ 2 +( x)^ 2 ...(1) Since _a^b f(x) d x= _a^b f(a+b-x) d x Hence I= _ / 6 ^ / 3 ( x)^ 2 d x ( x)^ 2 +( x)^ 2 ...(2) aligned & Equation (1)+(2), & I _ 1 / 3 ^ / 3 ( x)^ 2 ( x)^ 2 ( x)^ 2 ( x)^ 2 d x & I= 12 aligned Hence Assertion ' A ' is correct. aligned & Let P= _ / 6 ^ / 3 f(x) d x f(x)+f ( 2 -x ) ...(3) & P= _ / 6 ^ / 3 f ( 2 -x ) d x f(x)+f ( 2 -x ) ...(4) aligned Equation (3) + (4), 2 P= _ / 6 ^ / 3 d x P= 12 Hence Reason R is also true putting f(x)=( x)^ 2 in Reason ' R ' we g