Integral Finding

#643 / Math Medium

Solve the integral:

Expand Hint
$$$\int(3x^3+4x-5)dx=\int (3x^2)dx+\int (4x)dx-\int (5)dx$$$
Hint 2
$$$\int x^n \:dx=\frac{x^{n+1}}{n+1}$$$
This is a calculus problem, and can be written as:
$$$\int(3x^3+4x-5)dx=\int (3x^2)dx+\int (4x)dx-\int (5)dx$$$
The power rule:
$$$\int x^n \:dx=\frac{x^{n+1}}{n+1}$$$
Using the power rule to solve the problem’s integral:
$$$\int3x^3+4x-5)dx=\frac{3x^{(3+1)}}{(3+1)}+\frac{4x^{(1+1)}}{(1+1)}-5x$$$
$$$=\frac{3x^{4}}{4}+2x^2-5x$$$
Next, solve using the upper integral boundary of 1, and lower integral limit of -2:
$$$=\frac{3(1)^{4}}{4}+2(1)^2-5(1)-[\frac{3(-2)^{4}}{4}+2(-2)^2-5(-2)]$$$
$$$=\frac{3}{4}+2-5-[\frac{3(16)}{4}+2(4)+10]$$$
$$$=\frac{3}{4}+2-5-12-8-10=-32.25$$$
-32.25


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