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C1 Integration question help!!!

How do i go along to answer this and finding C?? I end up getting the wrong answer for C! please show me how to work this out!!
Thanks
Question is in attachment!!

Thanks in advance!

C1.JPG37.0KB

Reply 1

cpm1

You know that xrootx is x^3/2, yes?

Reply 2

MrEboueEmmanuel

integrate normally, then sub x=4, and make y=35, solve for C

Reply 3

ilyking

difficult to see the power of 5x, what is it?

EDIT: you might as well type it out for us

Reply 4

mujahid_e3

Original post by cpm1

You know that xrootx is x^3/2, yes?

yes when i integrated i got the following properly i get the following: 10x^1/2 +2/5x^5/2 +C

But then i know you have to find C but how do i do it? Please help!!!

Thanks

Reply 5

mujahid_e3

Original post by ilyking

difficult to see the power of 5x, what is it?

EDIT: you might as well type it out for us

its 5x^-1/2 + x root x

How to find C. can u kindly show me step by step!

Thanks

Reply 6

dstevens

Original post by mujahid_e3

yes when i integrated i got the following properly i get the following: 10x^1/2 +2/5x^5/2 +C

But then i know you have to find C but how do i do it? Please help!!!

Thanks

You are given in the question that

y=35

when

x=4

and you now have the equation for

y

so substitute the

x

and

y

values in.

C

is what you need to add to the

x

side with 4 substituted in to get 35.

C

is the constant of integration meaning that it remains constant regardless of the values you put in. Once you have found it, you can find y for any value of x.

Reply 7

mujahid_e3

Original post by dstevens

You are given in the question that

y=35

when

x=4

and you now have the equation for

y

so substitute the

x

and

y

values in.

C

is what you need to add to the

x

side with 4 substituted in to get 35.

C

is the constant of integration meaning that it remains constant regardless of the values you put in. Once you have found it, you can find y for any value of x.

so it would be:
35= 10 * 4^1/2 + 2/5 * 4 ^5/2 ?
this is 35= ????
im a bit stuck please help me complete!!
Thanks

Reply 8

united.spammers

Original post by mujahid_e3

so it would be:
35= 10 * 4^1/2 + 2/5 * 4 ^5/2 ?
this is 35= ????
im a bit stuck please help me complete!!
Thanks

10*4^1/2 is the same as 10*sqrt(4) which equals 20

4^5/2 is the same as sqrt(4^5) which is sqrt(1024) which equals 32

So you have 35=20+32+C and you can solve for C

Reply 9

sohail.s

can really read the dy/dx part, i think its 5x^1/2 + xrootx

if you integrate that you'll get 10x^1/2 + 2/5 x^5/2 + C

we're give than when x=4 y =35

substitue x=4 into that equation

so 20 + 12.8 + C = 35
therefore C = 2.2

is that right?

y = 10x^1/2 + 2/5 x^5/2 + 2.2

Reply 10

mujahid_e3

Original post by sohail.s

Yes your right i checked... But how did you get the C? i am a bit stuck!!! Because i wasnt sure how to work it out! can u plz show me?

Thanks

Reply 11

sohail.s

Original post by mujahid_e3

Yes your right i checked... But how did you get the C? i am a bit stuck!!! Because i wasnt sure how to work it out! can u plz show me?

Thanks

C is the constant of integration
to find C substitute youe value of x (given) into the equation you just found by integration
make the equation equal to the value of y (given) and solve to find C

after integrating

y= 10x^1/2 + 2/5 x^5/2 + C
we are told that y=35 when x=4

put x=4 into the equation y= (10*2) + (2/5 * 32) + C

y=35 so 20 + 12.8 + C = 35

therefore C = 2.2

so y= 10x^1/2 ~ 2/5x^5/2 + 2.2