Integration Jeopardy

Integration By Substitution

100

∫-15x⁴(-3x⁵-1)⁵dx

1/6(-3x⁵-1)⁶+C

200

∫x²(1+2x³)²dx

1/18(1+2x³)³+C

300

∫sin⁶(5x)cos(5x)dx

1/35(sin5x)⁷+C

400

∫x³√(x⁴+5)dx

1/6(x⁴+5)^3/2+C

500

∫(x+7)∛(3-2x)dx

-1/4(51/4(3-2x)^4/3-3/7(3-2x)^7/3)+C

Integration By Parts

100

∫xe^xdx

xe^x-e^x+C

200

∫(lnx)(x⁶)dx

1/7(lnx)x⁷-1/49x⁷+C

300

∫x²sin(4x)dx

-1/4(x²)cos4x+1/8(x)sin4x+1/32cos4x+C

400

∫x⁴sin(x)dx

-x⁴cosx+4x³sinx+12x²cosx-24xsinx-24cosx+C

500

∫e^2xsin(3x)dx

1/13e^2x(2sin(3x)-3cos(3x))+c

Partial Fractions

100

∫5/(2x²-3x-2)dx

-ln|2x+1|+ln|x-2|+C

200

∫8/(3x²+8x+4)dx

-2ln|x+2|+2ln|3x+2|+C

300

∫(4x-7)/(x²+9x+14)dx

7ln|x+7|- 3ln|x+2|+C

400

∫-2/(x²-4)dx

1/2ln|x+2| - 1/2ln|x-2|+C

500

∫(x⁴+3x³+2x²+1/x²+3x+2)dx

x³/3+ln|x+1|-ln|x+2|+C

Trig Substitution

100

∫1/(√(1-x²))dx

arcsin(x)+C

200

∫1/(1+x²)dx

arctan(x)+C

300

∫6/(3+3x²)+C

2arctan(x)+C

400

∫3/√(2x²)dx

3arcsin(x-1)+C

500

∫4/(√1-x⁴)dx

4arcsin(x²)+C

Bonus Trivia

100

An advanced mathematical science that speaks a single universal language

What is Calculus?

200

Using this type of approximation method will result in an underestimate on a strictly increasing function. 

What is a left-hand Riemann Sum

300

One of the uses of differential calculus is describing how steeply a curve is rising or falling. This is measured by a straight line which touches the curve at exactly one point

What is the Tangent line?

400

A scientist and mathematician that was one of several to develop a method, still used in introductory calculus classes, for obtaining the derivative of a curve from first principles

Who is Issac Newton?

500

 if f(x) is continuous over the closed interval [a,b] and differentiable over the open interval (a,b), then there exists a point c∈(a,b) such that the tangent line to the graph of f(x) at c is parallel to the secant line connecting (a,f(a))and (b,f(b)).

What is the Mean Value Theorem?