Integration
Riemann Sums
Miscellaneous
Summation Notation
Power Rule
100
int 5x^2 \ dx
5/3 x^3+C
100
If you are creating 6 rectangles that span an interval from [2,4], what is the width of each rectangle?
1/3
100
If the derivative determines instantaneous rate of change, the integral determines the...
area under the curve
or
accumulation of change
100
Determine 'Delta x' for the the summation notation of the following integral:
int_0^2 x \ dx
(2/n)
100
Solve the following definite integral using the power rule:
int_1^3 4 \ dx
8
200
int1/xdx
ln x +C
200
Find the exact value of:
int_0^12f(x)dx
-6
200
This theorem links the two "halves" of Calculus.
Fundamental Theorem of Calculus
200
Determine the 'generic x_sub i' for the summation notation of the following integral:
int_0^8 2x^2+6x \ dx
((8i)/n)
200
Solve the following indefinite integral using the power rule:
int \ 7x^6 \ dx
x7 + C
300
int_1^2 x\ dx
3/2
300
x: | 2 | 4 | 6 | 8 | 10 |
f(x):| 3 | 7 | 10 | 13 | 15 |
Use Left Riemann Sum to estimate the area with 4 subintervals for f(x) on the interval [2,10]
66
300
!!!!!!!!DAILY DOUBLE!!!!!!!!!!
Other than Newton, who "invented" Calculus?
Liebniz
300
Determine the 'x_sub i' for the summation notation of the following integral:
int_3^9 3/(x^3) +8x \ dx
(3+(6i)/n)
300
Solve the following definite integral using the power rule:
int_8^10 6x^2-12x+8 \ dx
776
400
inte^(5x)\ dx
1/5e^(5x) + C
400
Find the exact value of
int_0^12f(x)dx
-15/2+2\pi
400
Which is more accurate for a given number of rectangles - Left endpoint, Right endpoint or Midpoint approximations?
Midpoint
400
Determine the integral represented by the summation notation:
lim_(n->oo)sum_(i=1)^n (3((2+(2i)/n)^2)+(10(2+(2i)/n))+5)(2/n)
int_2^4 3x^2 + 10x +5 \ dx
400
Find the exact value of the following definite integral using the power rule.
int_1^4 sqrtx \ dx
14/3
500
intsinx-cosx\ dx
-cosx-sinx+C
500
Approximate the area under the curve over the interval [-3,2] using Right Riemann Sum. Let n = 5.
f(x)=x^2+2x+2
20
500
After which mathematician is the "sum of rectangles" technique named for?
Riemann
500
Determine the summation notation of the following integral:
int_5^12 sqrtx\ dx
lim_(n->oo) sum_(i=1)^n (sqrt(5+(7i)/n))(7/n)
500
Solve the following definite integral using technology. Round to the nearest whole number.
int_4^12 3/(x^2) - 12x^3 + x/9 \ dx
-61432