The average value is given by
Setting
, you get
, and the integral becomes
Answer:
(a) 0.4
(b) a = 3
Step-by-step explanation:
(a) The area under the curve from x=4 to x=6 is 0.2 units high and 2 units wide, so is 0.2·2 = 0.4. (The area of a rectangle is the product of length and width.)
(b) The area is 0.2 and the height of the curve is 0.2, so the width of the region of concern is 0.2/0.2 = 1. (Again, area = height·width, or width = area/height.) 1 unit from the left end is found at X=3, so a = 3.
Answer:
(x^4-8)^45 /180 +c
Step-by-step explanation:
If u=x^4-8, then du=(4x^3-0)dx or du=4x^3 dx by power and constant rule.
If du=4x^3 dx, then du/4=x^3 dx. I just divided both sides by 4.
Now we are ready to make substitutions into our integral.
Int(x^3 (x^4-8)^44 dx)
Int(((x^4-8)^44 x^3 dx)
Int(u^44 du/4)
1/4 Int(u^44 dul
1/4 × (u^45 / 45 )+c
Put back in terms of x:
1/4 × (x^4-8)^45/45 +c
We could multiply those fractions
(x^4-8)^45 /180 +c
Answer:
4.8 or 4 4/5
Step-by-step explanation:
