MHT CET202620 April 2026Morning ShiftMathematicsDefinite IntegrationActual
If ₀^1 dx x + 1 - x = 2 k , then the value of k is...
Options
- A4 3
- B4 3
- C2 3
- D2 3
Correct answer
B. 4 3
Step-by-step solution
Rationalizing the denominator of the integrand: ₀^1 dx x + 1 - x = ₀^1 x + 1 + x ( x + 1 )^2 - ( x )^2 dx = ₀^1 ( x + 1 + x ) dx Integrating with respect to x : = [ 2 3 (x + 1)^ 3/2 + 2 3 x^ 3/2 ]₀^1 Applying the limits: = ( 2 3 (2)^ 3/2 + 2 3 (1)^ 3/2 ) - ( 2 3 (1)^ 3/2 + 0 ) = 4 2 3 + 2 3 - 2 3 = 4 2 3 Equating to the given value 2 k : 2 k = 4 2 3 k = 4 3 Answer: 4 3