Definite Integrals
Areas
Volumes
Lengths of Curves
Fun
100
0∫2 4x3+2x+4 dx
28
100
Find the area of the region enclosed by y = x2 - 2 and y = 2
10 2/3
100
Find the volume of the solid generated by revolving y = x2 , y=0, and x=0 around the x-axis.
32π/5
100
Find the length of the curve y=x2 , -1≤x≤2
≈6.126
100
Which NFL quarterback has the most Super Bowl rings?
Tom Brady
200
0∫3 x3+5x+1 dx
34.5
200
Find the area of the region enclosed by y = 7-2x2 and y = x2+4
4
200
Find the volume of the solid generated by revolving the region bounded by y = sec x and y = √(n) (-π/4≤x≤π/4)around the x-axis.
π2-2π
200
Find the length of the curve y=sec x , -π/3≤x≤π/3
≈3.139
200
How many parsecs did the Millennium Falcon make the Kessel Run in?
12
300
0∫5 x4+2x3-x2+4x-6 dx
915.8333
300
Find the area of the region enclosed by y = 8 cos x and y=sec2 x , -π/3 ≤ x ≤ π/3
6√ (3)
300
Find the region of the solid generated by revolving the region enclosed by a triangle with vertices (1,0) , (2,1) , and (1,1) around the y-axis.
4π/3
300
Find the exact length of curve by antidifferentiation. y=(1/3)(x2+2)3/2 from x=0 to x=4
12
300
Who has the most Olympic gold medals and how many do they have?
Michael Phelps;23
400
1∫3 2x3+8x-9 dx
54
400
Find the area of the region enclosed by x = tan2y and x = -tan2y , -π/4≤y≤π/4
4 - π ≈ 0.858
400
Find the area of the surface found by revolving x = √(y) , 0≤y≤2 around the y-axis
≈13.614
400
Find the length of the curve f(x) = x1/3 + x2/3 , 0≤x≤2
≈3.6142
400

Ms. No’s favorite esports team is… (hint: it is owned by a streamer)

DSG

500
2∫3 4x4+3x2-4 dx
183.8
500
Find the area of the propeller-shaped region enclosed between the graphs of y = (2x)/(x2+1) and y = x3
ln 4 - (1/2) ≈ 0.886
500

find the volume of the solid generated by revolving the region bounded by y = √ (x), y=0, and x=4 around the y-axis.

128π/5

500
Find the length of the nonsmooth curve y = 4√ (x) from x=0 to x=16
≈16.647
500

Ms. No used to have a cool volunteer job in high school and college. What was it?

EMT

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