Calculus 2 EXAM 1 Practice

Draw the Region, the axis of revolution, specify the method, state the formula, solve

DO THIS FOR ALL OF THEM

A ball of radius 15 has a round hole of radius 5 drilled through its center. Find the volume of the resulting solid.

Find Answer

Arc Length (hard)

Find the arc length of the curve y=(1/8)(-x^2+8ln(x)) from x=2 to x=8

Area of surface of Revolution

Find the area of the surface obtained by rotating the curve y= 1+6x^2 from x=0 to x=9 about the y-axis

Area of Surface of Revolution

Find the area of the surface obtained by rotating the curve y=3x^3; from x=0 to x=7 about the x-axis

Arc Length

Find the length of the curve defined by y=6x^(3/2)+1 from x=1 to x=8

Cross-Section example about x-axis (using e)

Find the volume of the solid formed by rotating the region enclosed by y= e^(3x)+4, y=0, x=0, x=.6, about the x-axis

Cross-Section example about x-axis (harder)

Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by y=x^2 & y=3x , about the x-axis

Volume using shell method around y-axis

Find the volume of the solid generated by revolving the described region about the given axis. The region enclosed above by the curve y= 1+(x^2/4), below by the x-axis, to the left by the y-axis, and to the right by the line x=5, rotated about the y-axis

Volume using shell method around y-axis

Find the volume of the solid generated by revolving the described region about the given axis. The region enclosed by the curve y=sqrt(3x), the lines y=2x-3 and x=0 rotated about the y-axis

Volume using shell method around x-axis

Find the volume of the solid generated by revolving the described region about the given axis: The region enclosed by the curve x=sqrt(y), and by the lines x=-y, and y=5, rotated about the x-axis

Cross section about the y-axis

Find the volume of the solid obtained by rotating the region bounded by y=-5, y=1/x^3, y=0, x=3, x=5

Cross-Section example about x-axis (easy)

Find the volume of the solid obtained by rotating the region bounded by y=7x^2, x = 1, and y = 0, about the x-axis

Cross section about the y-axis

Find the volume of the solid obtained by rotating the region bounded by y=x^2, y=1; about y=7

Volume by Arc Length Method

L = ∫ sqrt(1+[f'(x)]^2) dx

Volume using shell method around the x-axis

The region between the graphs of y=x^2 and y=5 x is rotated around the line x=5.

Volume by Washer Method

V = ∫ (π[R(x)]^2-[r(x)]^2) dx

Volume by Shell Method

V = ∫ 2π (shell radius)(shell height) dx Shell height is usually X but in an example, we will see when it isn't X

Volume by Area of Surfaces of Revolution

V = ∫ 2π*f(x)*sqrt(1+[f'(x)]^2) dx

Volume Using Cross Section

V = ∫ A(x) dx

Volume by Disk Method

V = ∫ π[R(x)]^2 dx

Review the book if you can

review some of the set problems. SLEEP :)