Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202123 Aug 2021Evening ShiftMathematicsIndefinite IntegrationActual

If f^ (x)= ^2(x)+ ^2(x) and f ( 4 )=0 , then

Options

  1. A(x)- (x)-x+ 2
  2. B(x)- (x)-2 x+ 2
  3. C(x)+ (x)-2 x+ 2
  4. D(x)- cosec (x)-2 x+ 2

Correct answer

B. (x)- (x)-2 x+ 2

Step-by-step solution

f^ (x)= ^2 x+ ^2 x f(x)= ( ^2 x+ ^2 x ) d x aligned & = ( ^2 x ^2 x + ^2 x ^2 x ) d x & = ^4 x+ ^4 x ^2 x ^2 x d x & = ( ^2 x+ ^2 x )^2-2 ^2 x ^2 x ^2 x ^2 x d x aligned aligned & = 1 ^2 x ^2 x d x- 2 d x & = ^2 x+ ^2 x ^2 x ^2 x d x-2 x+C & = ^2 x d x+ cosec ^2 x d x-2 x+C aligned aligned & f(x)= x- x-2 x+C & f ( 4 )=0 aligned 4 - 4 -2 ( 4 )+C=01-1- 2 +C=0 C= 2 f(x)= x- x-2 x+ 2

Practice Indefinite Integration on Quantrex Academy →

More from Indefinite Integration

If 5 x x -2 dx = ax + b | x -2 x |+ c , then a + b = 2025x Cos ⁻¹ ( 1-x^2 1+x^2 ) d x(x>0)= 2025d x (1+ x ) x-x^2 = 2025If x x x+1 ~d x= f (x)+ k , then f ( 4 )= 2025If x^4+1 x^2+1 d x=A x^3+B x^2+C x+D Tan ⁻¹ x+E , then A+B+C+D= 2025If x^2-x+2 x^2+x+2 d x=x- (f(x))+ 2 7 Tan ⁻¹(g(x))+c , then f (-1)+ 7 ~g (-1)= 2025(x- 3 ) (x+ 6 ) d x= 2025If a x+3 x 5 x+2 x d x= 26 29 x- k 29 |5 x+2 x|+c , then |a+k|= 2025 Full Indefinite Integration list All AP EAMCET PYQs