Question

Find the average value (g ave) of the function g on the given interval.

g(x) = 2*​x^​(1/​3) [8,125]

Answer 1

Sol glas Given function gla) = 243 The average value of function on the interval [a,b ] is gave a g (4 dn 125 La 2x 3 che 8 3 TL Jo 39 c2+17128 % 3u - pe 33 + 1 8 a 42 (78 f (M) dua f(b) flas - (125) 33 (81413 - 78 78 625 625-88 78 547 - 7.8026 78 78 Now Average value of 9/4)= 7.8025 approy

Answer 2

SOLUTION :

Average value (g.)  of the given function g(x) in interval (1, 27)

   125

= ∫    g(x) dx  / (125 - 8)

   8

              125

= 1/117   ∫    2 (x^(1/3)  dx

               8

                                 125

= 2/117 * 3/4 [ x^4/3) ]                            

                                  8                                                      

= 3/234 * [125^(4/3) - 8^(4/3)]

= 3/234 * 609

= 7.807  (ANSWER)