Consider the given integral.
I=∫504√x+44√x+4+4√9−xdx ……. (1)
We know that
∫baf(x)dx=∫baf(a+b−x)dx
Therefore,
I=∫504√5−x+44√5−x+4+4√9−(5−x)dx
I=∫504√9−x4√9−x+4√4+xdx
I=∫504√9−x4√9−x+4√x+4dx …… (2)
On adding equation (1) and (2), we get
I=∫504√9−x+4√x+44√9−x+4√x+4dx
I=∫501dx
I=[x]50
I=5−0
I=5
Hence, this is the answer.