- #1

karush

Gold Member

MHB

- 3,269

- 5

$\textsf{The total area of the region bounded by the graph of $f(x)=x\sqrt{1-x^2}$ and the x-axis is}$

$$(A) \dfrac{1}{3}\quad

(B) \dfrac{1}{3}\sqrt{2}\quad

(C) \dfrac{1}{2}\quad

(D) \dfrac{2}{3}\quad

(E) 1 $$

find the limits of integration if

$$f(x)=0 \textit{ then } x=-1,0,1$$

so we have a symetric graph about $y=x$ so

$$\displaystyle

2\left|\int_{0}^1 x\sqrt{1-x^2}\,dx\right|

=2\left(

-\frac{1}{3}\left(1-x^2\right)^{\frac{3}{2}}

\right)\bigg|_{0}^1

=\dfrac{2}{3}\quad (D)$$ok hopefully this is the answer but I was alarmed how much time I spent on calculation

which will kill you on these exams even if you get the corrects answers.not real sure what the slam dunk method would be just from obersavation.