If f is continuous for all c, which of the following integrals necessarily have the same value?

Question

I. ∫_a^b f(x)dx

II. ∫₀^b-a f(x+a)dx

III. ∫_a+c^b+c f(x+c)dx

A) I and II only

B) I and III only

C) II and III only

D) I, II, and III only

E) No two necessarily have the same value

Answer 1

Hi Elijah H.,

If you substitute in the argument for f in each of these integrals, into the limits given, you will see that I and II reduce to integral (a to b). But III reduces to (a+2c to b+2c). 'Nuff said?

-- Cheers, -- Mr. d.