Unit 5: 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

∫cos²xdx [Hint: Use Power Reduction Identity  cos²x=(1+cos2x) /2]

(cosxsinx+x)/2+C

500

∫e^2xsin(3x)dx

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

Partial Fractions

100

∫5/(2x²-3x-2)dx

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

200

∫(10x-2x²)/(x-1)²(x+3)dx

ln|x-1|-2/(x-1)-3ln|x+3|+C

300

∫[(1/(1+x²)) + (1)/(x+1)(x-2)]dx

(8/3)ln|x+1|+arctanx-(5/3)ln|x-2|+C

400

∫((x³-7x²+10x+1)/(x²-7x+10))dx

(x²/2)-1/3ln|x-2|+1/3ln|x-5|+C

500

∫((x⁴+3x³+2x²+1)/(x²+3x+2))dx

x³/3+ln|x+1|-ln|x+2|+C

Inverse Trig

100

∫3/√(1-x²)dx

3arcsin(x)+C

200

∫(1/x√(x²-4)) dx

(1/2) arcsec (x/2) +c

300

∫(1/√(21-4y-y²)) dy

arcsin ((y+2)/5) +c

400

Evaluate the following integral from 0 to 1

∫5/(9x²+2)dx

(5/3√2)arctan (3/√2 )

500

∫[(x³ -x -1)/(x²+1)] dx

(1/2) x² -ln(x²+1) - 2arctan x +c

Bonus Trivia

100

An advanced mathematical science that speaks a single universal language

What is Calculus?

200

Differential and Integral

What are the two main branches of Calculus?

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

A special case of the Mean Value Theorem

What is Rolle's Theorem