MHT CET20249 May 2024Evening ShiftMathematicsDefinite IntegrationActual
The integral _ 6 ^ 4 d x 2 x ( ^5 x+ ^5 x ) is equal to
Options
- A1 5 ( 4 - ⁻¹ ( 1 3 3 ) )
- B1 10 ( 4 - ⁻¹ ( 1 9 3 ) )
- C1 20 ⁻¹ ( 1 9 3 )
- D40
Correct answer
B. 1 10 ( 4 - ⁻¹ ( 1 9 3 ) )
Step-by-step solution
aligned Let I & = _ 6 ^ 4 d x 2 x ( ^5 x+ ^5 x ) & = _ 6 ^ 4 ~d x 2 x x ( ^5 x+ 1 ^5 x ) & = 1 2 _ 6 ^ 4 ^2 x x ( ¹⁰ x+1 ^5 x ) d x & = 1 2 _ 6 ^ 4 ^4 x ^2 x ¹⁰ x+1 ~d x aligned Put ^5 x= t 5 ^4 x ^2 x ~d x= dt aligned I & = 1 2 _ 1 9 3 ^1 dt 5 t ^2+1 & = 1 10 [ ⁻¹ t ]_ 1 9 3 ^1 & = 1 10 [ ⁻¹ 1- ⁻¹ ( 1 9 3 ) ] & = 1 10 [ 4 - ⁻¹ ( 1 9 3 ) ] aligned