I'm guessing you mean
First, compute the quotient:
Split up the remainder term into partial fractions. Notice that
<em>x</em> ² + 4<em>x</em> + 3 = (<em>x</em> + 3) (<em>x</em> + 1)
Then
So the integral becomes
We can simplify the result somewhat:
Let's simplify step-by-step.<span><span><span><span>−12</span>−12</span>−<span>12x</span></span>+6</span><span>=<span><span><span><span><span><span>−12</span>+</span>−12</span>+</span>−<span>12x</span></span>+6</span></span>Combine Like Terms:<span>=<span><span><span><span>−12</span>+<span>−12</span></span>+<span>−<span>12x</span></span></span>+6</span></span><span>=<span><span>(<span>−<span>12x</span></span>)</span>+<span>(<span><span><span>−12</span>+<span>−12</span></span>+6</span>)</span></span></span><span>
=<span><span>−<span>12x</span></span>+<span>−<span>18</span></span></span></span>
Since V = (4/3) * pi * R^3
If R is halved, V' will reduce by a ratio of (1/2)^3 = 1/8
So V' = (1/8)V
Answer:
384mm
Step-by-step explanation:
