Area Calculation using Integrals: Finding the Minima of y=f(x)

[zorro]

Homework Statement

The area bounded by the curve y = f(x) = x⁴ -2x³ + x² + 3, the x-axis and the ordinates corresponding to the minimum of the function f(x) is?

The Attempt at a Solution

I found out the critical points as x= 0,1,1/2
Out of these, the minima occurs at 0 and 1

Since the question asks ordinates corresponding to the minimum, we get y = 0 for both x=0 and 1. Integrating from 0 to 0 is 0 offcourse. But the answer given is 91/30 which is obtained with limits 0 and 1 (which are abcissae). Is the question wording wrong?

 

[tiny-tim]

Hi Abdul!

hmm … yes of course, for a point (x₀,y₀), x₀ is the abscissa, and y₀ is the ordinate …

I think the question is using the word "ordinate" to mean the line to (x₀,y₀) which is parallel to the y-axis or ordinate-axis, ie the line x = x₀.

It's very confusing. And I thought everyone stopped using "ordinate" and "abscissa" about 50 years ago.

 

[zorro]

Yes that might be a possible reason. Thanks tiny-tim