Antiderivatives Exam! Review

Antiderivatives

100

Find the general solution of g(x) given that g'(x)=4x²

g(x)=(4(x^3)/3) + c

200

Find the Anti Derivative of 

g'(x)=cscxcotx+csc²x

g(x)=-cscx+cotx+c

300

Find the Antiderivative of 

K'(x)=3x²+4x

Find the particular solution that satisfies the initial condition (2,9).

K(x)=x³+2x²-7

400

Find the Anti Derivative of F'(x)=4^x

Find the particular solution that satisfies the initial condition 

F(0)=(1/ln(4)) +3.

F(x)=(4^x/ln(4)) + 3

500

Given that F''(t)=cos(t)

Find the particular solution that satisfies the initial condition F'(pi)=6 and F(0)=4

F(t)=-cos(t)+6t+5

Riemann Sums

100

Find the Left Reimann Sums of the Graph on the board between the interval [0,4] with 2 equal sub intervals

LRAM₂=18 units²

200

Find the Right Reimann Sums of the Graph on the board between the interval [1,7] with 3 equal sub intervals

RRAM₃=34 units²

300

Find the Midpoint Reimann Sums of f(x)=2x+3 between the interval [-2,4] with 3 equal sub intervals

MRAM₃=30 units²

400

Using the Trapezoidal Rule,

Approximate the Area of under the curve of f(x)=2x+3 from [-3, 5] using 4 equal sub intervals

T₄=40 units²

500

Using the Table on the board!

Find 

LRAM₅=

RRAM₂=

LRAM₅=600un²

RRAM₂=-500un²

Integrals

100

1)

(x⁶/3)-(x¹⁰/10)+7x+c

200

2)

2

300

3)

(7/4)x⁴-3x^-1-2x^-2+c

400

4)

(-1/4)cos(4x)+c

500

5)

(-1/4)(1+x⁴)^-1+c

Mixed!

100

Find the exact Area under the curve of f(x)=x² between the interval [-3,2]

35/3

or about 11.67

200

“To be or not to be” is a famous line from this Shakespeare play.

Hamlet

300

Find the Exact area under the curve of f(x)=234x⁵⁶⁷⁸/sin(45x)-3

between the interval [-2,-2]

0

400

What does "TV" stand for in reference to Taylor Swift's music?

"Taylor's Version" (AKA her re-recorded albums)

500

If you were to using U substituion to find the Anti derivative of 

F'(x)=cos³xsinx, 

What would "u" be and what would "du"

u=cosx

-1du=sinxdx

Random!

100

What Kate Bush song was featured in Season 4 of Stranger Things?

Running Up That Hill

200

Who are the three members of Boygenius?

Phoebe Bridgers, Lucy Dacus, Julien Baker

300

What is the name of the serial killer in the film The Silence of The Lambs?

Buffalo Bill

400

What kind of breakfast does Donkey want to make with Shrek in Shrek?

Waffles

500

In SpongeBob the Movie, Who's crown must SpongeBob get back?

King Neptune