Question

evaluate integral
http://www.webassign.net/cgi-bin/symimage.cgi?expr=int_1%5E64%20%281%20%2B%202%20root3%28x%29%29%2Fsqrt%28x%29%20dx

Answer 1

\[\sqrt{x}=x ^{1/2}\]Move denominator to numerator; multiply through.

Answer 2

ok i am stuck on this: \[(1/2)/(1/2)+2^{5/6}/(5/6)\left(\begin{matrix}64 \\ 1\end{matrix}\right)\]

Answer 3

\[= \int\limits_{1}^{64} ( x^{-\frac{1}{2} } + 2 ( x^{\frac{1}{3} - \frac{1}{2} } ) )\]

Answer 4

\[= \int\limits_{1}^{64} ( x^{-\frac{1}{2}} + 2 x^{ -\frac{1}{6} } )dx \]

Answer 5

so its not ^5/6?

Answer 6

When you swing it to the top the 1/2 becomes negative.

Answer 7

right

Answer 8

so now what i do?

Answer 9

wait i add one to each of the numorator?

Answer 10

You start over. Integrate what elecengineer did. The negative is not showing on exponents.

Answer 11

yes but then i have to add one which becomes: \[x^{1/2} /(1/2)+ 2^{5/6}/(5/6)\]

Answer 12

You are writing rubbish. What is 2^(5/60?)

Answer 13

so well can you show me please..so i can pick up where im going wrong

Answer 14

\[\int\limits_{1}^{64}x ^{-1/2}+2x ^{-1/6}\]The negative not showing in exponent.

Answer 15

ok so whats the next step

Answer 16

Exponent work\[-(1/2)+(2/2)=(1/2)\]\[-(1/6)+(6/6)=(5/6)\]

Answer 17

Got it?

Answer 18

yes thats what i did

Answer 19

next step please

Answer 20

Well, you are confusing yourself. Above, you left of the x. Then instead of dividing, just flip it and multiply; makes everything cleaner.\[2x ^{1/2}+[2(6)/5]x ^{5/6}\]

Answer 21

ok so you riciporcal the 5/6 to 6/5 and mulitiple by 2

Answer 22

Yes, the 2 is already there as a coefficient.

Answer 23

ok now i understand

Answer 24

so now its 2x^(1/2)+(12/5)x^(5/6) right

Answer 25

did you get this? it is a definite integral

Answer 26

\[\int _1^{64} \frac{1}{\sqrt{x}}dx =2\sqrt{x}|_1^{64}=2(\sqrt{64}-\sqrt{1})=2\times 7=14\]

Answer 27

im doin it differentlt like:
{2(8) + (12/5) (2^5)}-(22/5)

Answer 28

thats not right

Answer 29

\[\int_1^{64} \frac{2}{\sqrt[6]{x}}dx = \frac{12}{5}\sqrt[6]{x^5}|_1^{64}\]

Answer 30

\[=\frac{12}{5}(32-1)=74.4\]

Answer 31

so "final answer" should be
\[14+74.4=88.4\] unless i made an arithmetic mistake

Answer 32

now can you explain why you are integrating and also converting decimals to fractions? what kind of math is this???

Answer 33

this is calculus... and my textbooks shows me to do this

Answer 34

oh ok. usually converting decimals to fractions comes first.