# Calculus

posted by .

Integrals:

When we solve for area under a curve, we must consider when the curve is under the axis. We would have to split the integral using the zeros that intersect with the axis.

Would this be for all integrals? What if we just want to "find the integral", without finding it 'in terms of area'?

• Calculus -

No, not true for all integrals. But if you are looking for something that only has magnitude, you have to split the integrals, as the area below the axis is NEGATIVE.
On things like vector work (force*dx), the negative would mean work being absorbed, so it might be useful to not divide the integral if you were looking for net work done.

## Similar Questions

1. ### Calculus

Would someone clarify this for me... Is antiderivatives just another name for intergral and why is intergral of a function is the area under the curve?
2. ### Calc.

Find the area of the region bounded by the parabola y=x^2, the tangent line to this parabola at (1,1) and the x-axis. I don't really get what this question is asking. It looks like the area of right triangle to me...try the graph, …
3. ### calculus, volume , application of integration

show steps for the following: Consider the curve f(x)=x^4 between x = -1 and x = 4. a)What is the volume obtained by revolving the area under the curve around the x-axis?
4. ### math-plz help

Consider the curve f(x)=x^4 between x = -1 and x = 4. a)What is the volume obtained by revolving the area under the curve around the x-axis?
5. ### Calculus ll - Improper Integrals

Find the area of the curve y = 1/(x^3) from x = 1 to x = t and evaluate it for t = 10, 100, and 1000. Then find the the total area under this curve for x ≥ 1. I'm not sure how to do the last part of question ("find the the total …
6. ### Chemistry

My question is 'what does the area under the curve represent?
7. ### Calculus

1. Find the area of the region bounded by the curves and lines y=e^x sin e^x, x=0, y=0, and the curve's first positive intersection with the x-axis. 2. The area under the curve of y=1/x from x=a to x=5 is approximately 0.916 where …
8. ### brief calc

Calculate the total area of the region described. Do not count area beneath the x-axis as negative. Bounded by the curve y = square root of x the x-axis, and the lines x = 0 and x = 16 This is under Integrals, i don't know what i'm …
9. ### Fundamental Theorm of Calculus

Use a definite integral to find area of the region under the curve y=7-4x^2 and above the x-axis. Thanks in advance!
10. ### Calculus

Find the area cut off by x+y=3 from xy=2. I have proceeded as under: y=x/2. Substituting this value we get x+x/2=3 Or x+x/2-3=0 Or x^2-3x+2=0 Or (x-1)(x-2)=0, hence x=1 and x=2 are the points of intersection of the curve xy=2 and the …

More Similar Questions