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QUIZ MATH!!! Can y'all solve this ? Good luck ​

Answer»

Answer:

69.72

Step-by-step EXPLANATION:

\int\limits^4_1( {x\sqrt{x} + \frac{1}{x\sqrt{x}} } )^{<klux>2</klux>} \, dx

FIRST, \int\ ({x\sqrt{x} + \frac{1}{x\sqrt{x}} } )^{2} \, dx

= \int\ (x^{3} + \frac{1}{x^{3}} + 2) \, dx

=\int\ x^{3} \, dx + \int\ {x^{-3}} \, dx + \int\ 2 \, dx

=\frac{x^{4} }{4} + \frac{x^{-2} }{-2} + 2x

=\frac{x^{4} }{4} + \frac{-1}{2x^{2} } + 2x

Now,

\int\limits^4_1( {x\sqrt{x} + \frac{1}{x\sqrt{x}} } )^{2} \, dx      = [ \frac{x^{4} }{4} + \frac{-1}{2x^{2} } + 2x]⁴₁

= {(4⁴ - 1⁴)÷4} + {-1÷2(4²-1²)} + 2(4-1)

= \frac{255}{4} - \frac{1}{30} + 6

= \frac{3825 - 2 + 360}{60}

=\frac{4183}{60}

≈69.72


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