Question

What is the definite integral of `x^3` from 1 to 2?

Answer 1

Increment the exponent from 3 to 4. Also use the 4 as the denominator. Then substitute the boundaries into the function, where you have to subtract the lower boundary once substituted from the upper boundary once substituted. Then use basic algebra to evaluate.

`int_1^2 x^3dx=[(x^4)/4]_1^2=[((2)^4)/4 - ((1)^4)/4]=16/4 -1/4=15/4=3.75`

This image a graph of the function `x^3`. I zoomed in on Quadrant I and changed the window settings via the WINDOW button.