Answer
-429
Work Step by Step
Original Equation: $\int$ $(1+6w^{2}-10w^{4})dx$ on the interval $[3,0]$
To solve this integral, we first need to find the anti-derivative.
The anti-derivative of $x^{n}$ is found through the equation $\frac{x^{n+1}}{n+1}$. by applying this formula to each term in the equation, we see that the final anti-derivative is $w+\frac{6w^{3}}{3}-\frac{10w^{5}}{5}$ which can be reduced to $w+2w^{3}-2w^{5}$
Now that we have this equation, we simply subtract the bottom range from the upper range. Our range is $[3,0]$, so we plug 3 and 0 into the anti derivative and the difference of the two is our final answer.
$(3+2(3)^{3}-2(3)^{5})$-$(0+2(0)^{3}-2(0)^{5}$ $= -429$
