Department

MathematicsCourse Code

MATH 2BProfessor

AllStudy Guide

MidtermThis

**preview**shows page 1. to view the full**5 pages of the document.**●It’s the sum of the area of infinite rectangles under the function

●What is the area of each rectangle?

○(x)Δxf

●Therefore

○rea (x)dxA = ∫

b

a

f

●What then, is the volume of the area under the curve rotated around a line?

What is the Area Under the Curve?

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● π (R(x) (x)) dxV = ∫

b

a

2−r2

○Because the area of a circle is , we can compile an integral from this by usingrπ2

(x) r(x)R2− 2

Example #1

●Find the volume of a solid with a base of region R between , which and y xy = √x=

has cross-sections perpendicular to the x-axis in the shape of squares

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