Integration: F(x) = integral [from b to a] [(1/3) x^3] dx

[hyourinn]

\(\displaystyle F(x)= \displaystyle{\int^a_b \frac{1}{3}x^3 dx}\)

 

[Deleted member 4993]

\(\displaystyle F(x)= \displaystyle{\int^a_b \frac{1}{3}x^3 dx}\)

What was your question?

 

[Steven G]

\(\displaystyle F(x)= \displaystyle{\int^a_b \frac{1}{3}x^3 dx}\)

The left hand side is a function of x, while the rhs is a function of a and b which results in a constant. Is that what you wanted? After all, you never did ask a question!

 

[HallsofIvy]

IF you want simply the value of \(\displaystyle \int_b^a \frac{1}{3}x^3 dx\) then, since the anti-derivative of \(\displaystyle x^n\) is \(\displaystyle \frac{1}{n+ 1}x^{n+1}+ C\), \(\displaystyle \int_b^a \frac{1}{3}x^3d= \left[\frac{1}{12}x^4\right]_b^a= \frac{1}{12}(a^4- b^4)\). As others said, that is not a function of x.