need help with another problem TEST TODAY!! [[[HALP Me]]]]

[lunarskull]

i found another problem that i am completely stumped on. if someone could help me plz. feel free to ask me another question about calculus. i can only go up to math 150a which is mostly calc 1.

evaluate the definite integral by the limit definition

S(anti derivative sign)with 2 on top and 1 on bottom (of the sign) ((x^2)+1)

plz help me im desperate

 

[Guest]

the intergral of x^2 + 1 is

(1/3) x^3 + x + c

apply the range date of 2 and 1 to this equation

area = ((1/3) (2^3) + 2) - ((1/3) (1^3) + 1)

note the variable c disappears as it is on both sides ie c-c

area = ((1/3) (8) +2) - ((1/3) (1) + 1)

= 8/3 + 2 - 1/3 - 1
= 3 1/3
0r 10/3

 

[lunarskull]

damn, it seems i have to solve this problem using sigma and triangle x as well. so i have to use the limit definition, which is the really long way. if you could just start the first few steps of the problem for me, that would helpful.

definition of a definite integral:

lim_________n
a->0___(sigma sign)_____ f(C(sub i))((a)(x(sub i))
__________i=1

i hope that definition is not confusing. i put the lines underneath because html doesnt read long spaces

 

[Gene]

(D = delta = triangle)
y = ((x^2)+1)
y + Dy = ((x+Dx)^2+1 =
x^2+2x*Dx + Dx^2
subtracting
Dy = 2xDx + Dx^2