Integrating Polynomials: Practice Problems

[cd246]

Homework Statement

2. /int 1_0 (5u^7+pi^2) dx the answer is (5/8)+pi^2
3./int 4_0 (x^(1/2))(x+1) the answer is 272/15.

Homework Equations

The Attempt at a Solution

For 2. I already have the 5/8, my question do I integrate the pi^2? I tried integrating that with no success.

For 3. (x^(3/2)/3/2)((x^2/2)+x)
then (2x^(3/2)/3)((1/2)x^2+x)
plug 4: (16/3)(8+4=12)=192/3=64

 

[matness]

for 2: yes you integrate .Pi/2 is a constant.How do you integrate a constant.
for 3: your method is not acceptable.

If you take derivative of (2x^(3/2)/3)((1/2)x^2+x) you don't obtain
(x^(1/2))(x+1) But you should have done so.

So Try to expand (x^(1/2))(x+1) ( get rid of the paranthesis ) Then apply the rule you know about this type of integration.

note:
you can't integrate two parts separately. Remember for example how do you take derivative of product of functions. it is NOT just the product of derivatives of functions themselves.

 

[malawi_glenn]

How did you try?

/int 1_0 (5u^7+pi^2)dx ; where is the x? The variable of integration should be x..
Anyway, I assume that was a type-error.

pi^2 is just a constant...

for ./int 4_0 (x^(1/2))(x+1)

I assume you mean:

/int 4_0 (x^(1/2))(x+1)dx

Have you tried to multiply (x^(1/2)) into (x+1) ?

 

[cd246]

I found what i did wrong now. thanx