Integration?

Question

Hello. I Need Help In finding the area under a curve. I found the method of integration. The Graph is -7(x+7)^2-7 and the values that I am trying to find the area between are x=2 and x=7.

When I do it on my calculator the answer i get is 4736.67. When I try and do it step by step, i do not get that answer.

These are the links to my working out:
1)
http://img149.imageshack.us/img149/6588/mathssk5.jpg
2)
http://img291.imageshack.us/img291/5950/maths2sl5.jpg

Please Help.

Any Help or Contribution will be Appreciated.

Thanx.

Answer 1

i think u want to integrate ∫ -7(x+7)² - 7 dx (from 2 to 7)

∫ -7(x² +14x +49 ) -7 dx
∫ -7x² -98 x - 343 - 7 dx
∫ -7x² -98 x - 350 dx

now u have to integate every elements

[ -7x³ / 3 - 98 x² / 2 - 350x ] from 2 to 7
this is the correct answer for the integration,
and the solution in that link is wrong
when x = 7
u get (-5651.3)

when x = 2
u get ( -914.67)

so { -5651.3-(-914.67)}= -4736.63

Answer 2

A = - 7 ∫(x + 7)² + 1 dx between 0 and 7
A = - 7[ (x + 7)³ / 3 + x] between 0 and 7
A = - 7.[ (14)³ / 3 + 7 - 7³ / 3 ]
A = - 7[ 2744 / 3 + 21 / 3 - 343/3]
A = - 7 x 2422/3
A = - 5651units ² (to nearest whole number)
(ignore - ve sign)

Answer 3

The first link shows that when you worked out (x + 7)^2 you missed an x in the middle. It should be x^2 + 14x + 49.
If you want to be successful in this subject then in future you are going to have to avoid mistakes that simple.

Answer 4

with the intergration, its like integrate -7(x+7)^2 -7expand it, and it will be (-7)(x^2 +14x+7) -7.
and the answer will be -7[(x^3)/3 +7x^2 +7x] -7x with x=2 and x=7...

so the answer is (-7) [(343/3 + 686 + 49) - (8/3 + 56 + 14) + (-7(7) - (-7)(2)
= (-7) (335/3 +665) -35
= - 2345/3 - 4620
= -2345/3 - 13860/3
= -16205/3

cheers,
shaliney

Answer 5

first I would expand the expression:

y=-7(x+7)^2-7 between x=2 and x=7

y=-7(x^2+14x +49) -7

y=-7x^2 -98x -350
now integrate:

Area = -7/3x^3 -98/2x^2 -350x from x=2 to x=7

= (-7^4/3 -98*7^2/2-350*7)-(-7*2^3/3-98*2^2/2 -350*2)
=(-2401/3 -4802/2-2450)-(56/3-392/2-700)
=-781.666-2205-1750
=-4736.67

Your calculator appears to be correct!!!!!!!!!!!!!!!!!

Answer 6

Int [ -7(x+7)^2 -7 ]dx. ( 2
[ -(7/3)*(x+7)^3 -7x ] (2
- (7/3)*14^3 + 49 +(7/3)*9^3 -14

Answer 7

♥ no matter what we answer you are supposed to be the smartest;