5. Using the Fundamental Theorem of Calculus version I in (10.15):

(a) Confirm the formulas in exercise 1.

(b) Generalize exercise 1 to show that for a; b A R:

ð b a

cxn dx ¼

c n þ 1 ðbnþ1  anþ1Þ; n A R; n01:

(c) Confirm that for part (b), if n ¼ 1,

ð b a

cx1 dx ¼ c ln b

a

; b > a > 0:

(d) Generalize part

(c) if a < b < 0. (Hint: Compare

Ð b a cx1 dx to 

Ð b a cx1 dx to



Ð

a

b cx1 dx.)