can you help to solve this equation?

Question

Use the definition of area to show that the area under the curve y=x3
over the interval [0, b] is b4/4
(in this equation [0, b] is b4/4 ; b have power of 4 and then it is dividing with 4)
so please solve this equation.

Answer 1

~The area under a curve (f(x)) and between two vertical lines (y=a and y=b) is defined like the following:
Area = (from a to b)∫f(x).dx
Area = (from 0 to b)∫(x^3).dx = (from 0 to b)[(x^4)/4] = (b^4)/4 - 0 = (b^4)/4 I hope this helps.. I got it out of an old Math book.. <3

Answer 2

It's so simple:
The area under a curve (f(x)) and between two vertical lines (y=a and y=b) is defined like the following:
Area = (from a to b)∫f(x).dx
so
Area = (from 0 to b)∫(x^3).dx = (from 0 to b)[(x^4)/4] = (b^4)/4 - 0 = (b^4)/4