Answer:
x^2 - 12x..............................
 
        
             
        
        
        
You have to get from $30 to $21.75
21.75/30=0.725 x 100= 72.5% of the original price
        
             
        
        
        
∫(t = 2 to 3) t^3 dt 
= (1/4)t^4 {for t = 2 to 3} 
= 65/4. 
---- 
∫(t = 2 to 3) t √(t - 2) dt 
= ∫(u = 0 to 1) (u + 2) √u du, letting u = t - 2 
= ∫(u = 0 to 1) (u^(3/2) + 2u^(1/2)) du 
= [(2/5) u^(5/2) + (4/3) u^(3/2)] {for u = 0 to 1} 
= 26/15. 
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For the k-entry, use integration by parts with 
u = t, dv = sin(πt) dt 
du = 1 dt, v = (-1/π) cos(πt). 
So, ∫(t = 2 to 3) t sin(πt) dt 
= (-1/π) t cos(πt) {for t = 2 to 3} - ∫(t = 2 to 3) (-1/π) cos(πt) dt 
= (-1/π) (3 * -1 - 2 * 1) + [(1/π^2) sin(πt) {for t = 2 to 3}] 
= 5/π + 0 
= 5/π. 
Therefore, 
∫(t = 2 to 3) <t^3, t√(t - 2), t sin(πt)> dt = <65/4, 26/15, 5/π>.