Question

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Answer 1

Solution:- ∫ (1+sinx)dx

=> ∫√(1+sinx)×(1-sinx)/(1-sinx)dx

=>∫√ (1-sin²x)/(1-sinx)dx

=>∫√ (cos²x)dx/(1-sinx)

=>∫ cosx/√(1-sinx)____(1)

let (1-sinx) =t

d(1-sinx)/dt =dt/dt

=> -cosxdx=dt

From (1)

=> ∫-dt/√t from limit 0 to π/2 from given quest

=>[ -(t½)/1/2 ]₀ᵖⁱˡ²

=>put the value of t = 1-sinx

=>-2[(1-sinx)]₀ᵖⁱˡ²

=>-2[{1-sinπ/2}-{1-sin0}]

=>-2[(0)-1]

=> 2 Answer

_______________________________

Answer 2

Answer:

refer to this attachment ✅✅