Definite Integral

#308 / Math Medium

Solve the integral:

Expand Hint
$$$\int(5x^4-2x^2+1)dx=\int (5x^4)dx-\int (2x^2)dx+\int (1)dx$$$
Hint 2
$$$\int x^n \:dx=\frac{x^{n+1}}{n+1}$$$
This is a calculus problem, and can be written as:
$$$\int(5x^4-2x^2+1)dx=\int (5x^4)dx-\int (2x^2)dx+\int (1)dx$$$
The power rule:
$$$\int x^n \:dx=\frac{x^{n+1}}{n+1}$$$
Using the power rule to solve the problem’s integral:
$$$\int(5x^4-2x^2+1)dx=\frac{5x^{(4+1)}}{(4+1)}-\frac{2x^{(2+1)}}{(2+1)}+x$$$
$$$=\frac{5x^{5}}{5}-\frac{2x^{3}}{3}+x=x^5-\frac{2}{3}x^3+x$$$
Next, solve using the upper integral boundary of 5, and lower integral limit of -2:
$$$5^5-\frac{2}{3}\cdot 5^3+5-[(-2)^5-\frac{2}{3}(-2)^3+(-2)]$$$
$$$3125-\frac{2}{3}\cdot (125)+5-[(-32)-\frac{2}{3}(-8)-2]$$$
$$$=3125-83.33+5-[-32+5.33-2]=3,046.67-(-28.67)=3,075.3$$$
3,075.3


☕️ Donate to keep your study guide and instructor running!
🚨 [Beta] Test your FE exam readiness with a timed quiz!
☝️ Take the survey to help us improve!

< Prev #307

random #

#309 Next >