CALC 2 Stetson University Volume of The Cap of The Sphere of Radius R Questions I need you to answer these 10 question in a word document as soon as possib

CALC 2 Stetson University Volume of The Cap of The Sphere of Radius R Questions I need you to answer these 10 question in a word document as soon as possible Stetson University Summer Term 2020
Calculus II Exam #1
10 questions – Due Monday 6/15 by 11:59pm (submit to BB journals)
Name:
This work is to be done on your own – and without the help of another person
(other than me). You may use resources online, from your text, webassign,
etc. By signing this agreement to attest to this work being exclusively
yours.
Signature:____________________
#1. Find the area of the shaded region.
#2. Derive the volume of a sphere by revolving the semi-circle defined by
y = r 2 − x 2 about the x-axis where r is the (fixed) radius if the semicircle.
#3. Find the volume of the cap of the sphere of radius r. The height of the
cap is h. (See picture).
#4. Use the method of cylindrical shells to find the volume of the solid
torus indicated in the figure below.
#5. Evaluate
e
a
sin(b )d where a, b 
#6. Evaluate the integral
.
 ln(ax + b)dx where a, b 
.
#7. Evaluate the integral
 sin(ln x)dx
#8. Evaluate the integral
x
2
cos(mx)dx where m 
+
.
#9. Evaluate
r
2
ln(r )dr
#10. Evaluate the integral

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