integrationn

I_max = \frac{\pi }{4\sqrt{2}} ???

I _min = \pi /6??

x^{3} \leq x^{2}\; for\; x\;\in [0,1]

so\; 4-x^{2}-x^{3}\leq 4 - 2x^{2}

so\; \sqrt{4-x^{2}-x^{3} }\leq \sqrt{4 - 2x^{2} }

so\; \frac{1}{\sqrt{4-x^{2}-x^{3} } }\geq \frac{1}{\sqrt{4 - 2x^{2}} }

so\; \int_{0}^{1}{\frac{1}{\sqrt{4-x^{2}-x^{3} } } }\geq \int_{0}^{1}{\frac{1}{\sqrt{4 - 2x^{2}} } }

similarly use x^{3}\geq 0 \;for \;x\in [0,1]

so\; 4-x^{2}-x^{3} \geq 4-x^{2}

similarly we can find min and max of I₁

but how will we find I and I₁??

part 1 and 2 were my main dbt too [3]