Question

find the area enclosed between the curves y=3x and y=x^2

Answer 1

First you need to find the bounds of your integral. Solve, \[3x=x^2\] or \[x^2-3x=0\] which has roots at 0 and 3. (You can find these by the quadratic formula or by inspection) Now, the parabola opens up and the line cuts across it so we need to find:\[\int\limits_{0}^{3} (3x-x^2)dx\] take F(x)= \[\frac{3x^2}{2}-\frac{x^3}{3}\] evaluated F(3)-F(0)=(3/2)(9)-9=9(3/2-1)=9/2

Answer 2

do i need to draw the graph?

Answer 3

With these problems drawing the graph helps to see the correct order of subtraction. (In more complicated problems you might have functions that go above and under each other. In this case, you would need to split up the problem into separate integrations to find the total area) As long as the grader understands that you know the order of subtraction or you can just subtract however you like and take the absolute value since the problem asks for area specifically.

Answer 4

so the answer is final? please help if i was to draw a graph how would i go on succeeding in doing so

Answer 5

@keith27 Do you still need help?

Answer 6

yes i do chlorophyll

Answer 7

they want me to graph it out

Answer 8

Are you allowed to use graphic calculator?

Answer 9

or you prefer do manually?

Answer 10

manually and i dont no wer to begin

Answer 11

Since y = x² open up with its min O ( 0,0), while y = 3x is straight line go up through 0 (0.0) => the line above y = x².

Answer 12

Do you know how to draw a straight line???

Answer 13

yeah, wat bout it

Answer 14

k den is that all though?

Answer 15

after drawing straight lines will i be done?

Answer 16

NO,
First you draw BOTH graphs y = x², y = 3x
then, observe to see which on above to subtract the other
Let the different = 0 => 2 limits
Take finite Integral => Area ! DONE

Answer 17

oh ok il try doing that

Answer 18

@loggingin has already worked out in details. I just explained the steps!

Answer 19

ok den thanks