Hawken Spring Seniors vs. Basic Integral Calculus

The General Concept

100

The definite integral of a function on the interval [a,b] represents this on a graph.

What is the signed area under the curve from x=a to x=b?

200

In the definite integral  int_a^bf(x)dx , what are "a" and "b" called?

What are the "bounds of integration"?

300

This is how you estimate the accumulation for a rate function on a given integral.

What is "use a Riemann Sum"?

400

This is another name for an indefinite integral of a function.

What is the antiderivative of the function?

500

According to the FTC, the derivative of an integral function is this.

What is the original function?

Basic Integration Rules

100

 intkdx= 

What is kx + C

200

 intkf(x)dx= 

What is 

kintf(x)dx+C

300

 int(f(x)-g(x))dx= 

What is 

intf(x)dx-intg(x)dx

400

int_b^af(x)dx=

What is 

-int_a^bf(x)dx?

500

int_a^bf(x)dx-int_a^cf(x)dx=

What is 

int_c^bf(x)dx?

Riemann Sums

100

The primary use of Riemann sums is to find this

What is area under a curve?

200

This Riemann sum uses rectangles with length determined from the right side of a curve.

What is a Right Riemann Sum?

300

This Riemann sum uses rectangles with length determined from the left side of a curve.

What is a Left Riemann Sum?

400

This Riemann sum is the best estimate for 

int_a^bf(x)dx

What is the midpoint sum?

500

The left Riemann sum for a function on [a, b] is an overestimate for the area under the curve when this is true about the function.

What is "when f(x) is decreasing"?

Definite Integrals

100

int_0^2 6xdx=

What is 12?

200

int_-1^2(2x-1)dx=

What is nada, zilch, goose egg?

300

 int_-1^3(x^2+2x-8)dx= this

What is 

-44/3?

400

 int_0^3(e^x+e^3)dx= this.

What is 

4e^3-1

500

If a f(x) is an odd function, this is  int_-5^5(f(x))dx 

What is 0?

Indefinite Integrals

100

 int(3x^2-2x+10)dx= this

What is 

x^3-x^2+10x+C?

200

int((4x^2-x)/x)dx=this

What is 

2x^2-x+C?

300

int (x-2)(3x^2-7x)dx

What is 

3/4x^4-13/3x^3+7x^2+C?

400

 int(1/(2x+1))dx= this

What is 

1/2Lnabs(2x+1)+C?

500

int((sqrt(x))^3+2root4x-1/(x^2))dx

What is 

2/5x^(5/2)+8/5x^(5/4)+1/x+C?

Gettin Triggy with It

100

 int(cosx)dx= this.

What is 

sin(x)+C?

200

 int(2sinx)dx= this

What is 

-2cosx+C?

300

 int(sin(3x+1))dx= this

What is 

-1/3cos(3x+1)+C?

400

 int(4e^x-2sinx+cosx)dx= 

What is 

4e^x+2cosx+sinx+C?

500

 int(5tanxcosx)dx= this.

What is 

-5cosx+C?