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Please solve the integral problem . Definite integrals

Please solve the integral problem .
Definite integrals 

Question Image
Grade:12

3 Answers

Aditya Gupta
2080 Points
2 years ago
Differentiate both sides
f'(x)= 1/f(x)
Let y= f(x)
So ydy= dx
Integrating
y^2= 2x+C
At x=0, y=0
So C=0
So y=+-√(2x)
Put x=1, so minus sign gets rejected.
Therefore, f(x)= √(2x)
Shivanand
35 Points
2 years ago
But please explain how at X=0 y=0
Please explain his step I am not getting in this step properly
Minimum hundred words are required so I am just ffgbhhhg
Aditya Gupta
2080 Points
2 years ago
The reason for x=0 and y= 0 is as follows
In the equation given in the question we have
y= f(x)=∫0 to x of some function.
In this equation put x equal to zero.
f(0)= 0 because any integral from zero to zero obviously equals zero.

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