The diagram above shows the curve $\displaystyle y=2x^2-5x+5$ and straight line $\displaystyle y=5-x$.Find
(a)the points if intersection of the two graphs
i get the answer $\displaystyle (0,5)(2,3)$
(b)The area of the shaded region.
The diagram above shows the curve $\displaystyle y=2x^2-5x+5$ and straight line $\displaystyle y=5-x$.Find
(a)the points if intersection of the two graphs
i get the answer $\displaystyle (0,5)(2,3)$
(b)The area of the shaded region.
I've never really solved a problem like this before (or any integration problem actually) but would this work:
$\displaystyle \int_{0}^{3} 5-x\ dx-\left(\int_{0}^{3}5-x\ dx\ -\ \int_{0}^{3}2x^2-5x+5\ dx \right )$
Then do a similar thing for $\displaystyle x\in \left [ 3,5\right ]$ and add the results together.
this is my step to get the answer but the answer provided not same with my answer
$\displaystyle \frac{1}{2}(5)(5) - \left(\int_{0}^{5}(2x^2-5x=5) dx$
$\displaystyle =\frac{25}{2}-(\frac 2{x^3}{3}-\frac{5x^2}{2})_0^5$
$\displaystyle =\frac{25}{2}-({2(5)^3}{3}-\frac{5(2)^2}{2}=5(5))-0$
$\displaystyle =\frac{25}{2}-(\frac{275}{6}$
$\displaystyle =\frac{-33}{1}{3}$
is that correct??lol,my latex is wrong