CPM Homework Help : CALC3RD Problem 8-22

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8-22.

Multiple Choice: If $f$ is continuous for all $x$ , which of the following integrals must have the same value?

$\int _ { a } ^ { b } f ( x ) d x$

$\int _ { a + c } ^ { b + c } f ( x + c ) d x$

$\int _ { 0 } ^ { b - a } f ( x + a ) d x$

I and II only

I and III only

II and III only

I, II, and III

No two necessarily have the same value.

Hint:

Sketch a graph of I.
Then a transform it according to II. Is there a match?
Try again with III.

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