Definite Integrals
find -2∫4 |x| dx
10
u and dv for ∫x ln x dx
u=ln x and dv=x
Method that uses circles to calculate volume if there is a hole in the figure
washer method
The graphical depiction of a differential equation
Slope Field
4∫x2 (tan t) dt
2x tan(x2)
0∫pi (sin x+2) dx
2pi + 2
Trig substitution used for ∫1/√ (9-x2) dx
x=3sinθ
This integral is used to find areas between two curves with respect to y
What is a∫b (right - left) dy
s(t) if v(t) = 24t^3 - 12t^2 + 2t and s(1)=0
s(t) = 6t^4 - 4t^3 + t^2 - 3
the average value of a function
1/(b-a) a∫b f(x) dx
Approximation of the definite integral -2∫1 (x^2+2) dx with a Riemann sum using three equal subintervals and the right endpoints
8
∫(x-9)/(x2+3x-10) dx
2 ln|x+5| - ln|x-2| + C
Length of an arc of the parabola x=y2 from (0,0) to (1,1)
approximately 1.479
dx if you use Euler's Method to approximate y(2) using 4 steps given y(0)=1
dxd=0.5
1∫∞ 1/x2 dx
1
-1∫3 (2x+1)2 dx
57 1/3
∫x/(x2 - 1) dx
1/2 ln|x2 - 1| + C
Volume of the solid for the region bounded by y=√x and y=x rotated about the line y=1
pi/6
y if dy/dx = exy2
y= 1/(-ex + C)
d/dx [tan-1 (ex)]
ex/(1+e2x)
0∫3 f(x) dx = 1, 3∫7 f(x) dx = -4,
0∫1 f(x) dx = 2
7∫1 f(x) dx
5
∫ cos3x dx
sinx - (1/3) sin3x + C
Area bounded by y=x2 and y=2/(x2+1)
pi - 2/3
The difference when $3000 is invested at 5% interest for 2 years compounded weekly compared to compounded continuously
16 cents
1∫2 x√(x-1) dx
16/15