Question

4. Solve the definite integration of the followings:

(a) \(\int_{-2}^{2}\left(4 x^{2}-8 x\right) d x\)

(b) \(\int_{0}^{2} e^{2 x}-6 x d x\)

Answer 1

* @ s*(*- ) de u dhe 1 -2 = 4(8 +8) - 4(484) 4 x16.

6 (214) น. A 2. 3 - (1-2) - 3 (20) - (21) - 12. ๙ - - - -

Answer 2

SOLUTION :

a.

 2

∫    (4x^2 - 8x) dx

-2

                                  2

= [ 4/3 x^3 - 8/2 x^2]

                                 -2

= [((4/3 (2^3) - 4 (2^2)) - (4/3 (-2)^3) - 4 (-2)^2))]

= 32/3 - 16 - ( - 32/3 - 16)

= 32/3 + 32/3

= 64/3 =  21.333 (ANSWER).

b.

2

∫   (e^2x - 6x) dx 

0

                                     2

= [ 1/2 e^2x - 6/2 x^2 ]   

                                      0

= [ (1/2 e^(2*2) - 3 (2)^2) - (1/2 e^0 - 3 *0) ]

= e^4 / 2 - 12 - 1/2

= (e^4 - 25) / 2 

= 14.799  (ANSWER).