Need some assistance with a few calculus questions

[russjai]

Hi everyone, I have the answers for the following questions, I need the working out shown step by step. As i seem to get the incorrect answer. Not sure how to even start with the evaluation of integrals when in fraction form as below. Help very appreciated . Thanks

1. Evaluate the integrals

a.) (x^2+6)/(√x) dx (between 1 and 4)
ans = 24.4

b.) (2x)/(√1+2x) dx (between 0 and 4)
ans = 20/3


2.) The position function (in meters) of a particle is given by s=t^3-10.5t^2-2t t>0 . When does the particle reach a velocity of 52 m/s?

ans = 9



3. The Attempt at a Solution for Q.2

started by taking the derivative of s=t^3-10.5t^2-2t, Which gives Sv=3t^2-21t-2 .

I seem to get the wrong answer using algebra to solve t for 52= 3t^2-21t-2 .

Thanks in advance for your help.

Cheers

 

[tiny-tim]

welcome to pf!

hi russjai! welcome to pf!

(try using the X² icon just above the Reply box )

for 1a., split it into x² /√x and 1/√x

for 1b., do a substitution first, to make it like (a)

I seem to get the wrong answer using algebra to solve t for 52= 3t^2-21t-2 .

the method looks looks ok …

that's t² - 7t - 18 = 0 …

what did you get?​

 

[russjai]

Thanks for your quick response tiny-tim,

Ok i see where i went wrong with the algebra concerning Q.2 . I can now solve it to
t(t-7)=18 , Where 't' obviously = 9

For the 1st part regarding evaluating the integrals, still not too sure how to go about it would you possibly be able to show the working for Q.1) b.) (2x)/(√1+2x) dx (between 0 and 4)
From the start all the way to the answer 20/3 . ?

That would be extremely helpful.

Cheers

 

[tiny-tim]

… would you possibly be able to show the working for Q.1) b.)

not on this forum

make a substituion …

show us what you get ​