a-line-L-intersects-0-0-and-the-curve-y-x-2-at-x-t-What-is-the-equation-of-the-line-What-is-the-area-between-L-and-y-from-x-0-to-x-t-

Question Number 8070 by FilupSmith last updated on 29/Sep/16

a line L intersec t s (0, 0) a n d t h e c u r v e

y = x^{2} a t x = t .

What is the equation of the line ?

What is the area between L and y from

x = 0 to x = t ?

Answered by sandy_suhendra last updated on 29/Sep/16

s o t h e l i n e L i n t e r s e c t s (0, 0) a n d (t, t^{2})

t h e e q u a t i o n o f L \Rightarrow \frac{x - x_{1}}{x_{2} - x_{1}} = \frac{y - y_{1}}{y_{2} - y_{1}}

\frac{x - t}{0 - t} = \frac{y - t^{2}}{0 - t^{2}}

t x - t^{2} = y - t^{2}

y = t x

t h e a r e a b e t w e e n L a n d y

=_{0} \int^{t} (t x - x^{2}) d x

= {[\frac{1}{2_{}} {t x}^{2} - \frac{1}{3} x^{3}]}_{0}^{t}

= \frac{1}{2} t^{3} - \frac{1}{3} t^{3} = \frac{1}{6} t^{3}