AP EAMCET202018 Sep 2020Evening ShiftMathematicsIndefinite IntegrationActual
( ₀^k( k - t )^2 d t= )
Options
- A( k^2 2 )
- B( k^2 4 )
- C( k^2 6 )
- D( k^2 8 )
Correct answer
C. ( k^2 6 )
Step-by-step solution
( aligned ₀^k( k - t ) d t & = ₀^k(k+t-2 k t ) d t & = (k t+ t^2 2 )₀^k-2 k ( t^ 1 2 +1 1 2 +1 )₀^k & = (k k+ k^2 2 )- 4 k 3 (k^ 3 2 )₀^k & = 3 k^2 2 - 4 k 3 k^ 3 / 2 = k^2 6 aligned ) Hence, option (c) correct.