Calc 2 Jeopardy

You got this

100

Integrate 

∫(4x^2+x+3)dx

4/3x^3+x^2/2+3x+C

200

Integrate 

∫(2x-9 sin⁡x )dx

x^2 + 9cosx+C

300

Integrate 

∫(t+e^t )dt

t^2/2+e^t+C

400

Integrate 

∫(10/x) dx

10ln|x| + C

500

Integrate 

∫[6(5^x) dx]

6(5^x)/ln(5) + C

Definite-ly Fun

100

Use the Fundamental Theorem of Calculus to evaluate  ∫(3+x)dx  on [0,8]

56

200

Use the Fundamental Theorem of Calculus to evaluate  ∫(4x^3-2x)dx  on [-1,1].

0

300

Use the Fundamental Theorem of Calculus to evaluate  ∫(xsqrt(x)) dx on [4,9].

422/5

400

Use the Fundamental Theorem of Calculus to evaluate  ∫(3/x)dx  on [1,6]

3ln(6)

500

Use the Fundamental Theorem of Calculus to evaluate  ∫x(x^2-6)dx  on [-2,1]

21/4

Substitute it

100

Integrate 

∫[x^2/(sqrt(x^3+3))]dx

2/3 sqrt(x^3+3)+C

200

Integrate 

∫[x(1-3x^2)^4]dx

(-1/30)(1-3x^2)^5 +C

300

Integrate 

∫[(sinx)^3cosx]dx

(1/4)(sinx)^4+C

400

Integrate 

∫[xe^(-3x^2)]dx

 

(-1/6)e^(-3x^2)+C

500

Integrate 

∫[(x+1)5^[(x+1)^2]]dx

(1/2ln5)(5^[(x+1)^2])+C

Trig and Polar

100

Use the Fundamental Theorem of Calculus to evaluate  ∫cos(x/2)dx  on  [0,pi]

2

200

Give two polar representations of the cartesian point (1,-sqrt(3))

(2,-pi/3) and (-2, 2pi/3)

300

Use the Fundamental Theorem of Calculus to evaluate  ∫(secx)^2dx  on  [-pi/4,pi/4] 

2

400

What shape does the polar equation r=theta make?

Archimedes' Spiral

500

Integrate

∫x/(sqrt(1-x^4))

(1/2)arcsin(x^2)+C

Serie ously

100

If the common ratio is less than 1, what does the geometric series converge to?

a/(1-r²)

200

{a_n} = {3n/n²+1}
What is the third term in the sequence

9/10

300

True or False

If {a_n} and {b_n} both converge, then {a_n+b_n} must converge.

True

400

Prove if the Series {Sum (n⁷\7ⁿ)} converge?

Ratio Test: 1/7 < 1

500

What is the Mclaurin Series of Cos(x)

1-x²/2+x⁴/4+...