What's the difference between definite integration and indefinite integration?
I know indefinite integration involves u-substitution, but can someone expand on these definitions? Thanks!
I know indefinite integration involves u-substitution, but can someone expand on these definitions? Thanks!
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how about i give you some examples?
∫x dx = (1/2)x^2 + C is an indefinite integral
1
∫ x dx = (1/2)x^2 is a definite integral
0
the key is the lower and upper limit. If they are there, it's definite integral. If they're not there, it's indefinite integral
there are some exceptions
∞
∫1/x^2 dx is called improper integral
0
Edit:
please clarify your question. I'm not sure if i understand it.
Edit:
well, if they give you the lower and upper limit, then yes.
1
∫x dx = (1/2)x²
0
use the Fundamental theorem of calculus
b
∫f(x) dx = F(b) - F(a)
a
F is the integral of f
we just found F = (1/2)x²
(1/2)(1)² - (1/2)(0)²
(1/2) - 0
(1/2)
thus,
1
∫x dx = 1/2
0
∫x dx = (1/2)x^2 + C is an indefinite integral
1
∫ x dx = (1/2)x^2 is a definite integral
0
the key is the lower and upper limit. If they are there, it's definite integral. If they're not there, it's indefinite integral
there are some exceptions
∞
∫1/x^2 dx is called improper integral
0
Edit:
please clarify your question. I'm not sure if i understand it.
Edit:
well, if they give you the lower and upper limit, then yes.
1
∫x dx = (1/2)x²
0
use the Fundamental theorem of calculus
b
∫f(x) dx = F(b) - F(a)
a
F is the integral of f
we just found F = (1/2)x²
(1/2)(1)² - (1/2)(0)²
(1/2) - 0
(1/2)
thus,
1
∫x dx = 1/2
0
-
Definite, you don't have to include the constant term
Indefinite, you have to include the constant term
That will be enough for you to pass grade 12 calc class.
Indefinite, you have to include the constant term
That will be enough for you to pass grade 12 calc class.
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indefinite integration there is one constant if more then one then we put one constant.
Definitie integration there is a upper and lower limits so there no constant require.
Definitie integration there is a upper and lower limits so there no constant require.