Question

evaluate the integral

Answer 1

try wolfram

Answer 2

12/5 x^(5/2) [25,81]

Answer 3

Yeah. I think tonks method is accepetable.

Answer 4

Im not sure what you did :/

Answer 5

You can just input x inside the sqrt sign. making it integral of 6x^3/2

Answer 6

much lower than what you had, elaornelas

Answer 7

x = √x^2
x*√x = x^3/2

Answer 8

\[6\int\limits_{81}^{25} x ^{\frac{ 3 }{ 2 }}dx\]

Answer 9

hm I'm sorry I'm still kind of confused :/

Answer 10

i understand why you moved the 6, but not sure how to go about getting the solution from here

Answer 11

\[6\frac{ x ^{\frac{ 5 }{ 2 }} }{ \frac{ 5 }{ 2 } }] (81.25)\]

Answer 12

the integrand, 6x√x can be rewritten as 6x^(3/2) or 6x^1.5 then the power rule for anti-derivatives can be applied.

Answer 13

Just apply algebra. We know that xsqrt(x) = x^1 (x)^1/2 --> adding their exponents will yield to x^(1+(1/2)) or x^(3/2) or simply sqrt(x^3)

Answer 14

@elaornelas do you follow?

Answer 15

so so!

Answer 16

So what's next?

Answer 17

ok well let me show you what i have written down

Answer 18

\[-6\int\limits_{25}^{81}x(x)^{\frac{ 1 }{ 2 }}\]

Answer 19

Treat the x like it has an exponent of one and add the exponents (same base) to make it one term.

Answer 20

Why -6? Shouldn't be + And just simplify the expression \[x(x)^{\frac{ 1 }{ 2 }}\]
this is actually same to \[x ^{\frac{ 3 }{ 2 }} = \sqrt{x ^{3}}\]

Answer 21

negative is fine because she switched the bounds

Answer 22

yes exactly @Tonks

Answer 23

oops, sorry I didn't see that. my bad :D

Answer 24

its fine! @Yttrium :)

Answer 25

So you get it now, why it became sqrt(x^3)??

Answer 26

@elaornelas do you get the x^(3/2) (same question)?

Answer 27

yes i do @Tonks so would this mean my result would be \[\frac{ -12x ^{\frac{ 5 }{ 2 }} }{ 5 }\]???

Answer 28

yes: -12/5 x^(5/2) [25,81]

Answer 29

Yeah :D

Answer 30

-12/5* 55924
blech!

Answer 31

yay! @Tonks @Yttrium :)
OK so NOW….. is this the correct setup
-[F(b)-F(a)]=__?

Answer 32

gotta go, good luck, you two!

Answer 33

Owyeah :D

Answer 34

ok well i got this real weird number :/ "134217.6"

Answer 35

uh oh is that wrong?

Answer 36

not sure :/ I'm confused @Yttrium

Answer 37

\[\int\limits 6x \sqrt{x } dx=\frac{12 x^{5/2}}{5} \]\[\left(\frac{12\ 25^{5/2}}{5}\right)-\left(\frac{12\ 81^{5/2}}{5}\right)=-\frac{671088}{5} \]

Answer 38

The fraction to 10 digits.\[N\left[-\frac{671088}{5},10\right]=-134217.6000 \]