Double Jeopardy

4.4 "The 1st Fundamental Thm."

100

Evaluate the definite Integral

₀                

∫ (x-2)dx

^-1               

-5/2

Double Jeopardy: Points 2x

200

Evaluate the definite integral

₄                            

∫ (x-2)/(√ x)dx

¹                            

2/3

Double Jeopardy: Points 2x

300

Evaluate the definite integral

₃                   

∫ l2x- 3ldx

⁰                   

9/2

Double Jeopardy: Points 2x

400

Daily Double

Find the average value of the f'n over the interval and all values of x in the interval that the f'n equals the value.

f(x)=sinx; [0,pi]

(Calculator Allowed) (Three Decimal Places)

y=2/pi

x~0.690

x~2.451

Misc. (Motion)

100

A particle moves on the x-axis so that its velocity at any time t is given by v(t)=sin2t. At t=0, the particle is at the origin.

For 0<t<pi, find all values of t for which the particle is moving to the left

(pi/2)<t<pi b/c v(t)<0

Double Jeopardy: Points 2x

200

A particle moves on the x-axis in such a way that its position at time t is given

x(t)=(2t- 1)(t- 1)²

When is the particle at rest

t=2/3, 1 b/c v(t)=0

Double Jeopardy: Points 2x

300

Daily Double

A particle moves on the x-axis in such a way that its position at time t is given

x(t)=(2t- 1)(t- 1)²

At what time during (2/3)<t<1 is the particle moving most rapidly?

t=5/6

400

A particle moves on the x-axis so that its velocity at any time t is given by v(t)=sin2t. At t=0, the particle is at the origin.

For 0<t<(pi/2), find the average value of the position function

1/2

Double Jeopardy: Points 2x

4.5 "Integration by Substitution"

100

Evaluate the indefinite integral

∫ (1+ 2x)⁴(2)dx

[(1+2x)⁵/5]+ c

Double Jeopardy: Points 2x

200

Evaluate the indefinite integral

∫ (csc²x)/(cot³x)dx

[1/2(cotx)²]+ c

Double Jeopardy: Points 2x

300

Evaluate the indefinite integral

∫ cot²xdx

-cotx- x+ c

Double Jeopardy: Points 2x

400

Evaluate the indefinite integral

∫ (x²+3x+7)/(√ x)dx

(2x^5/2/5)+ (2x^3/2)+ 14x^1/2+ c

Double Jeopardy: Points 2x

4.1 "Anti-derivatives and Indefinite Integration"

100

Evaluate the indefinite integral

∫ ³√ (x²)dx

[(3x^5/3)/5]+ c

Double Jeopardy: Points 2x

200

Evaluate the indefinite integral

∫ (sec²x- sinx)dx

tanx+ cosx+ c

Double Jeopardy: Points 2x

300

Evaluate the indefinite integral

∫ [(sinx)/(1-sin²x)]dx

secx+ c

Double Jeopardy: Points 2x

400

Evaluate the indefinite integral

∫ [(x²+x+1)/(√ x)]dx

[(2x^5/2)/5]+ [(2x^3/2)/3]+ 2x^1/2+ c

Double Jeopardy: Points 2x