2 simple integration questions (help) (1 Viewer)

[Pace_T]

hey could you help me with these two questions:
1) 1~2 (2x - 1)^2 dx

2) 2~0 (4x^3 + x^2 + 5x)/x dx

by the way, 1~2 and 2~0 are the integration symbols
thanks!

 

[Slidey]

1) exapnd integrand to get: 4x^2-4x+1
2) cancel integrand: 4x^2 + x + 5

Now integrate:

1) [4x^3/3 - 2x^2 + x] 1 to 2 = -(4/3 - 2 + 1) + (32/3 - 8 + 2) = 13/3 #
2) [4x^3/3 +x^2/2 + 5x] 0 to 2 = -(0) + (32/3 + 2 + 10) = 68/3 #

I'm assuming that you meant 0 to 2 for number 2. Otherwise multiply by negative 1.

EDIT: Just realised x=0 produces a discontinuity for number 2, but x=0 is one of its terminals. Oh well.

 

[Pace_T]

thanks for your help