Use the properties of integrals to verify the inequality without evaluating the integrals. integrate from `int_0^1 sqrt(1+x^2)dx lt int_0^1...

You should
remember that `a dx.`

Notice that 0<1 and you need to verify if `sqrt(1+x^2) < sqrt(1+x)
` over the interval [0,1] such that:

If `x in [0,1] => x^2 < x =>
x^2 + 1 < x + 1 => sqrt(x^2 + 1)

Since `sqrt(x^2 +
1)

`sqrt(x^2 + 1) int_0^1 sqrt(x^2 + 1) dx < int_0^1
sqrt(x+1)dx`

Hence, using the properties of integrals yields
that inequality `int_0^1 sqrt(x^2 + 1) dx < int_0^1 sqrt(x+1) dx` 
holds.