Answer to Question #287102 in Calculus for Fauth

Question

MR=6+10x-18x^2

X=1

Sh 4000

Find total revenue

Answer 1

$MR=6+10x-18x²$

($MR$ represents Marginal Revenue)

$MR=\frac{dR}{dx}$

($R$ represents Total revenue)

Integrating both sides,we have

$\int{MR} dx+k=R$

$\implies R=\int{MR}dx+ k$

$=\int(6+10x-18x²)dx+k$

Using sum rule,

$=\int6dx+\int10xdx-\int18x²dx+k$

$=6x+5x²-6x³+k$

Since $R=0$ when $x=0$ ,then $k=0$

$\implies R=6x+5x²-6x³$