Home
Class 12
MATHS
Evaluate int(2)^(3) (sqrt(x))/(sqrt(5-x)...

Evaluate `int_(2)^(3) (sqrt(x))/(sqrt(5-x) +sqrt(x))` dx

Text Solution

Verified by Experts

The correct Answer is:
`((1)/(2))`
Let `I=int_(2)^(3)(sqrt(x))/(sqrt(5-x)+sqrt(x))dx` . . . (i)
`rArrI=int_(2)^(3)(sqrt(2+3-x))/(sqrt((2+3)-(5-x))+sqrt(2+3-x))dx`
`rArr I=int_(2)^(3)(sqrt(5-x))/(sqrt(x)+sqrt(5-x))dx` . . . (ii)
On adding Eqs . (i) and (ii) , we get
`2I=int_(2)^(3)(sqrt(x)+sqrt(5-x))/(sqrt(5-x)+sqrt(x))dx rArr 2I = int_(2)^(3)1 dx =1 rArr I=(1)/(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Evaluate int_(1)^(2)(sqrt(x)dx)/(sqrt(3-x)+sqrt(x)) .

Evaluate int_(0)^(a)(sqrt(x))/(sqrt(x)+sqrt(a-x))dx

int_(1)^(2)(sqrt(x))/(sqrt(3-x)+sqrt(x))dx .

Evaluate: int_(2)^(3)(sqrtx)/(sqrt5-x+sqrtx) dx.

Evaluate int_(0)^(3) (sqrtx dx)/(sqrtx + sqrt(3 - x)

Evaluate int_(1)^(5)sqrt(x-2)sqrt(x-1)dx .

Evaluate int_(0)^(1)(dx)/(sqrt(x+1)+sqrt(x)) .

By using the properties of definite integrals, evaluate the integrals int_(0)^(a)(2sqrt(x))/(sqrt(x)+sqrt(a-x))dx

Evaluate : int(x-3)sqrt(x+2)dx