Question

Please help - Curve Question involving differentiation

Answer 1

Typing out the question now!

Answer 2

A Curve C is defined for \[x >0\] by the equation \[y=x+1+\frac{ 4 }{ x^2 }\], find \[\int\limits_{?}^{?} (x+1+\frac{ 4 }{ x^2 }\] and hence find the area of the region bound by X, the lines x=1 and x=4 and the x-axis

Answer 3

"region bound by X" ? Do you mean the curve?

Answer 4

Yes Sorry!

Answer 5

Well there's no differentiation involved here, so the title is a bit misleading.

At any rate, you're asked to evaluate the definite integral,
\[\int_1^4\left(x+1+\frac{4}{x^2}\right)\,dx\]
which is just a matter of applying the power rule to each term. What are you having trouble with?

Answer 6

Oh, so the lines x=1 and x=4 are your boundaries?

Answer 7

Yes

Answer 8

The area you're computing: