What is the antiderivative of (16 - x)^(3/2)?
1 Answer
Jan 29, 2016
Explanation:
Antiderivative is just the integration. For handling this type of problem, you should be comfortable with the power rule.
color(red)(intquad x^n dx = x^(n+1)/(n+1)+C
Our problem we have to find
intquad(16-x)^(3/2) dx
We shall use a
Let
Differentiating with respect to
-dx= du
dx=-du
Our integral now becomes
intquadu^(3/2)(-du)
=-intquad u^(3/2)du
Use the power rule
=-u^(3/2+1)/(3/2+1) +C
=-u^(5/2)/(5/2)+C
=-2/5u^(5/2)+C
Substituting back for
=-2/5(16-x)^(3/2) + C