Solve the following definite integral from x=2 to x=-1: ((x^4) + 3(x^2) + 2) dx

GENERAL PROCEDURE --

To solve this equation you can separate and integrate each term on its own and then add each integral together.

To find the definite answer:

Substitute "x=2" into the integrated equation to get a value (y). Repeat this step by substituting in "x=-1" to get another value (z).

To calculate the final answer you take value z from y.

SOLUTION --

To integrate: Raise the power of "x" by 1 and divide by this raised number

i.e. Integral of (x^4) = (x^5)/5 Integral of 3(x^2) = (x^3) Integral of 2 = 2x

To find the general integral, add these terms together to find that "y = (x^5)/5 + x^3 + 2x"

Now substitute x=2 in to find the y-value: (2^5)/5 + (2^3) + 2(2) = 92/5 Then substitute x=-1 in to find the z-value: (-1^5)/5 + (-1^3) + 2(-1) = -16/5

Finally, take the z-value from the y-value. (92/5) - (-16/5) = 108/5 = 21.6