Help
Options
Didn't know it?
click below
click below
Knew it?
click below
click below
Don't Know
Remaining cards (0)
Know
retry
shuffle
restart
0:00
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.
Normal Size Small Size show me how
Normal Size Small Size show me how
Calculus 2 Midterm
| Question | Answer |
|---|---|
| For an integral from a to b, what is 1dx? | (1)b-(1)a |
| For an integral from a to b, what is xdx? (1. For a=0, and 2. For a≠0) | For a=0: b^2/2. For a≠0, (b^2-a^2)/2 |
| What is the antiderivative of ln(x)? | 1/x |
| What must you add after solving an indefinite integral? | +c!! |
| What is the antiderivative of 1? Why? | X (because x^0=1) |
| What is the integral of x^n(dx)? Example: x^2 | x^(n+1)/(n+1)… ex: (x^3)/3 |
| How do you change the limits of integration for u-sub? | Plug limits into x for u (ex: for u=x+9 on [0,1], u=9 and u=10. So (u^6)/12 = [(10^6) - (9^6)] / 12 |
| What is the formula for integration by parts? | (Integral of udv) = uv - (integral of vdu) |
| What is the formula for partial fractions? | P(x)/Q(x) = A/(x-r) + B/(x-s) |
| How can you tell if you should use partial fractions? | When it’s a polynomial over a polynomial |
| How do you evaluate an improper integral for c to infinity? | 1.) sub infinity for a. 2.) integrate. 3.) evaluate for ](c to a). 4.) Think about a->infinity |
| How do you evaluate an improper integral for infiniy to infinity? | Split it up into an integral (-infinity to 0) + integral (0 to infinity). Proceed with the ‘a—> infinity’ method for each, |
| What is the formula to find the area between curves? | integral (a to b) of [f(x)-g(x)]dx |
| What shape of graph comes from a quadratic equation? | U (parabola) |
| How does one find the points on a graph of a parabola? | the absolute min/max, and the zeroes on the x-axis |
| What is the quadratic equation? | For ax^2 + bc + c: x= [-b +/- sq root of (b^2) - 4ac ]/2a |
| What is the equation to find the absolute minimum/max on a parabola? | x= -b/2a |
| What is the formula for finding the average value of an integral? | [1/(b-a)] * integral of a to b of f(x)dx |
| What is the difference between an integral and a derivative? What clues are there to tell you which to use? | An integral describes the entire area under a curve. A derivate is like a ‘packaged’ downsized version. When something is going to a lower power, it’s being derived (packaged), and when it’s going to a higher power, it’s being integrated (expanded) |
| What method should you use to solve the integral of 3x^2 * sin(x^3)dx? | U-sub is best here, with u=x^3 and du=3x^2 dx |
| What method should you use to solve the integral of x * cos(x)dx? | Integration by parts |
| What is the fundamental theorem of calculus? | For an defined integral (a to b) of f(x)dx, once you’ve integrated it, the answer is F(b)-F(a) |
| For the s c -s -c rule, if the letters are stacked top down, which way is integration and which way is deriving? | Integration is moving upwards, and deriving is moving downwards |
| What is the range of the two axis of the unit circle? | From 0 to pi (right to left) and pi/2 to 3pi/2 (top to bottom) |
| What is the integral of 1/x? | ln(x) |
| Which trig identities correspond to x and y on the unit circle coordinates? | (x, y) = (cos, sin) |
| What is ln(1), and why? | ln(1)=0 because e^0=1 |
| What is the trig identity for sinx/cosx? | tanx |
| What is the trig identity for cosx/sinx? | cotx |
| What is the trig identity for 1/sinx? | cscx |
| What is the trig identity for 1/cosx? | secx |
| What is d/dx arctanx? | 1/(1+x^2) |
| What is d/dx arcsinx? | 1/(sq rt of (1-x^2) |
| What is d/dx arccosx? | -1/(sq rt of (1-x^2) |
| What is the formula for the Riemann sum? | the sum from i to n of f(x*) times delta x |
| When using the Riemann sum to estimate area, if we set n=3, what is delta x? (For [0,1] | Delta x would be 1/3 in this case |
| What is the formula to get volume (using an integral)? | [integral from a to b) A(x)dx |
| What are the coordinates of the unit circle, starting at 0 and going counterclockwise? | (1,0); (0,1): (-1,0); (0,-1) |
| Which trig identities add up to 1? | sin^2(x)+cos^2(x) |
Created by:
clownestate