Question

Show that ∫01 dx/√(-logx) =√π

Answer 1

Answer:

hello , let J= -3∫3(5x4/1+e-x)dx …..(1)

now, we know by properties of definite integral that we can replace the fn f(x) inside by f(a+b – x) or f( – 3+3 – x)= f( – x)

so, J= -3∫3(5( – x)4/1+ex)dx

or J= -3∫3(5x4/1+ex)dx ….....(2)

now, write (1) as J= -3∫3(5ex.x4/1+ex)dx …......(3)

add (2) and (3)

2J= -3∫3(5x4/1+ex)*(1+ex)dx = -3∫35x4dx = x^5| – 3 to 3= 2*3^5

or 2J= 486

so that J = 243

kindly approve :))

Step-by-step explanation:

i just give the step .