AP Calc AB Final Project - Integrals Jeopardy

Definite

100

The integral from 0 to 3 of (x-1)dx.

What is 3/2.

200

The integral from 0 to 4 of (2x+5)dx.

What is 36?

400

The definite integral from 6 to 7 of (x^1/2+x^-1/2)²dx refers to this value (simplest form).

What is 8.5 + ln(7/6).

500

The value of a if the definite integral from -a to a of e^xdx is equal to 1 refers to this expression (positive).

What is ln((1 + 5^1/2)/2).

Indefinite

100

The indefinite integral of 4x³(x⁴) is equivalent to this expression.

x⁴/2 + C

200

The indefinite integral of (5x-18)dx.

5x²/2 -18x + C

400

The indefinite integral of (x³-3x²+4x-9)/(x²+3) dx is equivalent to this expression.

What is .5x² - 3x + ln(x²+3) + C.

500

The integral of x(x-2)/(x-1)³dx.

What is ln|x - 1| + 1/(2(x - 1)²) + C.

Trig Integrals

100

The integral of tan(5x)dx.

What is 1/5 * sec²(5x) + C

200

The integral from 0 to pi/2 of cos(x)*sin⁴(x)dx.

What is 1/5.

300

The integral of sin(5x)sin(cos(5x)) dx.

What is ⅕ * cos(cos(5x)) + C.

400

The integral of 11sec(11x)tan(11x) dx.

What is sec(11x) + C.

500

The integral of cos(5x) / (3+sin(5x)) dx.

What is 1/15 * ln (abs(3+5sin(5x))) + C.

Exponential Integrals

100

Integral from 0 to 2 of e^2x dx

What is (e4-1)/2?

200

The integral of 2^x dx.

What is 2^x/ln(2) + C.

400

The integral from -1 to 2 of 1/e^x dx.

What is -e² + e.

U-Subs

100

Integral from 0 to 2 of (2x)dx

What is 1?

200

Integral from 0 to 2 of (3x+7)²

What is 206?

400

The integral from 0 to 8 of x(4e^x*x+3) dx (note x*x refers to x²).

What is 2e⁶⁷-2e³.