Question

integral problem

Answer 1

\[\int\limits_{?}^{?} \sqrt(x^2+4)/2x\]

Answer 2

dx

Answer 3

do i use tangent or secant for this problem?

Answer 4

how do i know when to use each?

Answer 5

@freckles i need help please

Answer 6

\[x^2+4=4(\frac{x^2}{4}+1)=4([\frac{x}{2}]^2+1)\]
recall \[\tan^2(\theta)+1=\sec^2(\theta)\]

Answer 7

\[4(\tan^2(\theta)+1)=4 \sec^2(\theta) \\ \text{ and we have } 4([\frac{x}{2}]^2+1)=4 \sec^2(\theta) \text{ when } \tan(\theta)=?\]

Answer 8

so it can be a+u^2 and still be tangent?

Answer 9

yep tangent
tan(theta)=x/2

Answer 10

okay and when is it secant?

Answer 11

is it u^2-a or a - u^2?

Answer 12

1-sin^2(theta)=cos^2(theta)
so
when a^2-u^2 do sin sub

1+tan^2(theta)=sec^2(theta)
a^2+u^2 do tan sub


tan^2(theta)=sec^2(theta)-1
u^2-a^2 do sec sub

where u is a function of x

Answer 13

okay it is so much clear now thank you again

Answer 14

let me know if you any further help

Answer 15

thanks will do