The General Concept
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?
intkdx=
What is kx + C
The primary use of Riemann sums is to find this
What is area under a curve?
int_0^2 6xdx=
What is 12?
int(3x^2-2x+10)dx= this
What is
x^3-x^2+10x+C?
int(cosx)dx= this.
What is
sin(x)+C?
In the definite integral int_a^bf(x)dx , what are "a" and "b" called?
What are the "bounds of integration"?
intkf(x)dx=
What is
kintf(x)dx+C
int_-1^2(2x-1)dx=
What is nada, zilch, goose egg?
int((4x^2-x)/x)dx=this
What is
2x^2-x+C?
int(2sinx)dx= this
What is
-2cosx+C?
This is how you estimate the accumulation for a rate function on a given integral.
What is "use a Riemann Sum"?
int(f(x)-g(x))dx=
What is
intf(x)dx-intg(x)dx
int_-1^3(x^2+2x-8)dx= this
What is
-44/3?
int (x-2)(3x^2-7x)dx
What is
3/4x^4-13/3x^3+7x^2+C?
int(sin(3x+1))dx= this
What is
-1/3cos(3x+1)+C?
This is another name for an indefinite integral of a function.
What is the antiderivative of the function?
int_b^af(x)dx=
What is
-int_a^bf(x)dx?
This Riemann sum is the best estimate for
int_a^bf(x)dx
What is the midpoint sum?
int_0^3(e^x+e^3)dx= this.
What is
4e^3-1
int(1/(2x+1))dx= this
What is
1/2Lnabs(2x+1)+C?
int(4e^x-2sinx+cosx)dx=
What is
4e^x+2cosx+sinx+C?
According to the FTC, the derivative of an integral function is this.
What is the original function?
int_a^bf(x)dx-int_a^cf(x)dx=
What is
int_c^bf(x)dx?
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"?
If a f(x) is an odd function, this is int_-5^5(f(x))dx
What is 0?
int((sqrt(x))^3+2root4x-1/(x^2))dx
What is
2/5x^(5/2)+8/5x^(5/4)+1/x+C?
int(5tanxcosx)dx= this.
What is
-5cosx+C?