SOLUTION: Evaluate exactly the value of the integral from negative 1 to 0 of the product of the cube of the quantity 4 times x to the 6th power plus 2 times x and 12 times x to the 5th power

Algebra ->  Finance -> SOLUTION: Evaluate exactly the value of the integral from negative 1 to 0 of the product of the cube of the quantity 4 times x to the 6th power plus 2 times x and 12 times x to the 5th power      Log On


   

Question 1029789: Evaluate exactly the value of the integral from negative 1 to 0 of the product of the cube of the quantity 4 times x to the 6th power plus 2 times x and 12 times x to the 5th power plus 1, dx. Your work must include the use of substitution and the antiderivative.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
int%28%28%284x%5E6%2B2x%29%5E3%2812x%5E5%2B1%29%29%2Cdx%2C-1%2C0%29
Let u=4x%5E6%2B2x,
du=%2824x%5E5%2B2%29dx
du%2F2=%2812x%5E5%2B1%29dx
Check the limits, when x=0, u=0
When x=-1, u=4-2=2
Substituting,


int%28%28%284x%5E6%2B2x%29%5E3%2812x%5E5%2B1%29%29%2Cdx%2C-1%2C0%29=-u%5E4%2F8%2BC
int%28%28%284x%5E6%2B2x%29%5E3%2812x%5E5%2B1%29%29%2Cdx%2C-1%2C0%29=-2%5E4%2F8
int%28%28%284x%5E6%2B2x%29%5E3%2812x%5E5%2B1%29%29%2Cdx%2C-1%2C0%29=-16%2F8
highlight%28int%28%28%284x%5E6%2B2x%29%5E3%2812x%5E5%2B1%29%29%2Cdx%2C-1%2C0%29=-2%29