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December 6th, 2007, 06:38 PM   #1
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Fundamental Theorem of Calculus

can anyone help me with these 3 questions

Use the fundamental theorem of calculus to show that:

a<b

b a
int f(x)dx = -int f(x)dx
a b





b b
int kf(x)dx = Kintf(x)dx
a a




a<c<b
c b b
intf(x)dx+intf(x)dx = intf(x)dx
a c a
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December 6th, 2007, 06:41 PM   #2
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I cant get the a's and b's to line up. They should be over the int's (for integral)
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December 7th, 2007, 05:06 PM   #3
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Quote:
Originally Posted by mrguitar
Use the fundamental theorem of calculus to show that:

a<b

* *b * * * * * * * * a
f(x)dx = - f(x)dx
* *a * * * * * * * * b



* *b * * * * * * * * * *b
Kf(x)dx = K f(x)dx
* *a * * * * * * * * * *a



a<c<b
* *c * * * * * * * b * * * * * * * b
f(x)dx + f(x)dx = f(x)dx
* *a * * * * * * * c * * * * * * * a
What progress have you made so far?
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December 9th, 2007, 02:22 PM   #4
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If F'(x)=f(x) then:

a
∫f(x)dx=F(a)-F(b)
b

This should solve all of them!
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