MHT CET202122 Sep 2021Evening ShiftMathematicsIndefinite IntegrationActual
_ 6 ^ 2 cosec x x 1+ cosec ^2 x d x=
Options
- A4 - ⁻¹ 2
- B⁻¹ 1
- C⁻¹ 2
- D⁻¹ ( 1 3 )
Correct answer
D. ⁻¹ ( 1 3 )
Step-by-step solution
Let I= _ 6 ^ 2 cosec x x 1+ cosec ^2 x d x Put cosec x=t cosec x x=-d t . When x= 6 , t=2 and when x= 2 , t=1 aligned & I = ₂^1(-1) dt 1+ t ^2 & = ₁^2 dt 1+ t ^2 = [ ⁻¹ t ₁^2= ⁻¹(2)- ⁻¹(1)= ⁻¹ [ 2-1 1+(2)(1) ]= ⁻¹ ( 1 3 ) . aligned