• Support PF! Buy your school textbooks, materials and every day products Here!

Integrate the following equations using U-Substitution

  • Thread starter Xetman
  • Start date
  • #1
8
0

Homework Statement


Integrate √(x2(x+3)) from -3 to 0.

0
∫√(x2(x+3)) dx
-3


2. The attempt at a solution
Here is what I did:
√(x2(x+3))
= x√(x+3)

Let u=x+3, du=dx, x=u-3
Insert the bounds and change the bounds to: 0 to 3.

x√(x+3)=
(u-3)√(u)
= u3/2-3u1/2

Thus we have:
3
∫(u3/2-3u1/2) du
0

Finally:

(2u5/2)/5-(2u3/2) from 0 to 3.
Thus I get: -4.15.

However the correct answer is positive 4.15.
I know the answer should be positive but what I don't understand is why I'm getting a negative answer. Please help.
Thanks in advance.
 

Answers and Replies

  • #2
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,224
947

Homework Statement


Integrate √(x2(x+3)) from -3 to 0.

0
∫√(x2(x+3)) dx
-3

2. The attempt at a solution
Here is what I did:
√(x2(x+3))
= x√(x+3)

Let u=x+3, du=dx, x=u-3
Insert the bounds and change the bounds to: 0 to 3.

x√(x+3)=
(u-3)√(u)
= u3/2-3u1/2

Thus we have:
3
∫(u3/2-3u1/2) du
0

Finally:

(2u5/2)/5-(2u3/2) from 0 to 3.
Thus I get: -4.15.

However the correct answer is positive 4.15.
I know the answer should be positive but what I don't understand is why I'm getting a negative answer. Please help.
Thanks in advance.
Be careful.

[itex]\displaystyle \sqrt{x^2} = |x|[/itex]

In fact, for x<0, [itex]\displaystyle\ \sqrt{x^2} = -x\ .[/itex]
 
  • #3
Dick
Science Advisor
Homework Helper
26,258
618

Homework Statement


Integrate √(x2(x+3)) from -3 to 0.

0
∫√(x2(x+3)) dx
-3


2. The attempt at a solution
Here is what I did:
√(x2(x+3))
= x√(x+3)

Let u=x+3, du=dx, x=u-3
Insert the bounds and change the bounds to: 0 to 3.

x√(x+3)=
(u-3)√(u)
= u3/2-3u1/2

Thus we have:
3
∫(u3/2-3u1/2) du
0

Finally:

(2u5/2)/5-(2u3/2) from 0 to 3.
Thus I get: -4.15.

However the correct answer is positive 4.15.
I know the answer should be positive but what I don't understand is why I'm getting a negative answer. Please help.
Thanks in advance.
It's positive because if x is negative then sqrt(x^2)=(-x). Right?
 
  • #4
8
0
Oh yeah. Silly mistake XD thanks.
 

Related Threads for: Integrate the following equations using U-Substitution

  • Last Post
Replies
2
Views
937
Replies
4
Views
1K
Replies
13
Views
5K
  • Last Post
Replies
1
Views
417
Replies
13
Views
15K
Replies
12
Views
774
Replies
1
Views
842
Top