Question-203835

Question Number 203835 by patrice last updated on 29/Jan/24

Answered by MathematicalUser2357 last updated on 30/Jan/24

b r u h

Commented by Frix last updated on 30/Jan/24

{It}^{'} s not that hard \dots

Answered by MrGaster last updated on 03/Nov/24

= \int_{0}^{\sqrt{2}} \frac{\sqrt{6 - \sqrt{{(5 x^{2} - 6)}^{2}}}}{\sqrt{5}} d x

= \int_{0}^{\sqrt{2}} \frac{\sqrt{6 - {(5 x^{2} - 6)}^{2}}}{\sqrt{5}} d x

= \int_{0}^{\sqrt{2}} \frac{\sqrt{6 - (6 - 5 x^{2})}}{\sqrt{5}} d x

= \int_{0}^{\sqrt{2}} \frac{\sqrt{5 x^{2}}}{\sqrt{5}} d x

= \int_{0}^{\sqrt{2}} \frac{\sqrt{5} x}{\sqrt{5}} d x

= \int_{0}^{\sqrt{2}} x d x = \frac{x^{2}}{2} ∣_{0}^{\sqrt{2}}

= \frac{{(\sqrt{2})}^{2}}{2} - \frac{0^{2}}{2}

= \frac{2}{2}

= 1

Commented by Frix last updated on 03/Nov/24

{(5 x^{2} - 6)}^{2} = 25 x^{4} - 60 x^{2} + 36 \neq 25 x^{4} - 50 x^{2} + 36

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