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If the integral [0,3] of f(x)dx=4, the integral [3,6] of f(x)dx=4, and the integral [2,6] of f(x)dx=5, then what does the integral [0,2] of f(x)dx=?

Answer 1

Cameron Alexander

What a great question!

It is #int_0^2 f(x)dx = 3#,

#int_0^3 f(x)dx = 4#, #int_3^6 f(x)dx = 4#, what do I get if I add these two integrals?

I get the integral: #int_0^6 f(x)dx#

And if I subtract this one:

#int_2^6 f(x)dx = 5#

from the sum I found above, what do I get?

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Answer 2

Paisley Johnson

The integral of ( f(x) ) from 0 to 2 is 3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.