Integrals!

Normal

100

Integral of (6x^2 - 3)dx

What is 2x^3 + 3x + C

200

Integrate 5

What is 5x + C

300

Integral of (x^2 - x) / x^(1/2)

What is x^(5/2)/(5/2) - x^(3/2)/(3/2) + C

400

Integral of (x^3 -x +2)/ (x^1/2)

What is (2/7)x^7/2 - (2/3)x^(3/2) + x^1/2

500

Integrate (x^2 - 6x + 5)/ (x + 6)

What is x^2/2 - x + C

Trigonometry

100

Integral of sin(2x) dx

What is -(1/2)cos(2x) + C

200

Integral of cos(x) - sin(x)

What is sin(x) + cos(x) + C

300

Integral of sin(x) + sec^2(x)

What is tan(x) - cos(x) + C

400

integral of 1/csc(x)

What is -cos(x) + C

500

Integral of sin(ln(x))/x

What is -cos(lnx) + C

Special Case

100

Integral of 3/x

What is 3ln|x| + C

200

Integral of e^(5x+2)

What is (1/5)e^(5x+2) + C

300

Integral of 1/sqrt(1-x^2)

What is sin^-1(x) + C

400

Integral of ln(7)*7^x

What is 7^x + C

500

Integral of x^2 + 6x + 5 + C

What is (1/3)x^3 + 3x^2 + 5x + Cx + D

Definite

100

Integral of 3x dx from [0,1]

What is 3/2

200

Integral of cos x dx from [0, pi]

What is 0

300

Integral of e^x from [-3, 3]

What is e^3 - 1/e^3

400

Integral of 1/xdx from [1,e]

What is 1

500

Integral of e^x + 1 from [0, ln(3)]

What is 2 + ln(3)

Warmup & Final Jeopardy

300

Turn in homework!

Warmup: The integral of 4x^3 - 3x^2 + 7x + 5

Today's groups: Meaylene/Axel/Cristian, Kip/Katie/Manny, Lez/Marley/Klyd, Mia/Jorge/Emily

What is x^4 - x^3 + 7x^2/2 + 5x + C

500

Final Jeopardy: Find f(x) if f'(x) = 4x + 7 and f(x) passes through the point (3, 41)

What is 2x^2 + 7x + 2