Integral Jeopardy!

Definite Integrals

100

₀∫² 4x³+2x+4 dx

28

200

₀∫³ x³+5x+1 dx

34.5

300

₀∫⁵ x⁴+2x³-x²+4x-6 dx

915.8333

400

₁∫³ 2x³+8x-9 dx

54

500

₂∫³ 4x⁴+3x²-4 dx

183.8

Areas of regions

100

Find the area of the region enclosed by y = x² - 2 and y = 2

10 2/3

200

Find the area of the region enclosed by y = 7-2x² and y = x²+4

4

300

Find the area of the region enclosed by y = 8 cos x and y=sec² x , -π/3 ≤ x ≤ π/3

6√ (3)

400

Find the area of the region enclosed by x = tan²y and x = -tan²y , -π/4≤y≤π/4

4 - π ≈ 0.858

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

Volumes around an axis

100

Find the volume of the solid generated by revolving y = x² , y=0, and x=0 around the x-axis.

32π/5

200

Find the volume of the solid formed by rotating the region bounded by y=x, between x=0 and x=2 about the Y-AXIS

8π/3

300

Find the region of the solid generated by revolving the region enclosed by a triangle with corners at (1,0) , (2,1) , and (1,1) around the y-axis.

4π/3

400

Find the area of the surface found by revolving x = √(y) , 0≤y≤2 around the y-axis

≈13.614

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

MATThematics

100

What is Matt's favorite color?

Blue

200

What section is Matt the captain of in the Spirit of Stony Brook Marching Band

Drumline

300

Name at least one of Matt's roommates and what subject they teach

Jayden (History of EOP), Andrew (Chemistry), Diego (Chemistry), Aaron (SA)

400

What town is Matt from?

Commack, NY (Go Cougars!)

500

What is Matt's two favorite mathematical applications

Logarithms and Differentiation