Question

Evaluate the integral from 0 to 3 of the quotient of x and the square root of the quantity x squared plus 16, dx.

a: 1
b: 2
c: 3
d: 4

Answer 1

this?
\(\huge \int_{0}^{3}\frac{x}{\sqrt{x^2+16}}\)

Answer 2

if that is so, then the variable change \(x^2+16=u\) and \(2xdx=du\) should do the job

Answer 3

so after the substitution you get:
\(\huge\frac{1}{2}\int_{16}^{25}\frac{du}{\sqrt{u}}\)

Answer 4

which integrated directly

Answer 5

yeah with a dx to the right of it :)

Answer 6

@myko

Answer 7

@Nnesha @miss.happy @Michele_Laino

Answer 8

I think that the result of @myko is right

Answer 9

the options are 1, 2, 3, or 4 :)

Answer 10

please use this identity:
\[\int {\frac{{du}}{{\sqrt u }}} = 2\sqrt u \]

Answer 11

what would i get as an answer? btw when myko asked: "this?" it was missing a dx next to it :)

Answer 12

Please I can not give you the answer directly since the Code of Conduct

Answer 13

okay can u plz write me the steps then? :)

Answer 14

ok!

Answer 15

please you have to compute this:
\[\left. {\sqrt u } \right|_{16}^{25}\]

Answer 16

how do i do so? :)

Answer 17

since we can write:
\[\frac{1}{2}\int {\frac{{du}}{{\sqrt u }}} = \sqrt u \]

Answer 18

hint:
\[\left. {\sqrt u } \right|_{16}^{25} = \sqrt {25} - \sqrt {16} = ...?\]

Answer 19

1 :) thank u !! i have 2 more if u dont mind?

Answer 20

ok!