# Calc II Cheat Sheet

Calculus 2 Final Exam Review –
Calculus 2 Final Exam Review –

This is a draft cheat sheet. It is a work in progress and is not finished yet.

### Trig Integrals

 ∫sinx dx = -cosx dx + C ∫cosx dx = sinx dx + C ∫sec2x dx = tanx dx + C ∫tanx dx = ln|secx| + C ∫secx tanx dx = secx + C ∫csc2x dx = -cotx + C ∫cscx cotx dx = -cscx + C ∫cotx dx = ln|sinx| + C

### Trig Identities

 ∫(1/x2 + a2) dx = 1/a tan-1(x/a) + C ∫(1/Sqrt(a2 – x2) dx = sin-1(x/a) + C

### Area Between Curves

 ```Area = ∫[Height] Width A = ∫(f(x) - g(x)] dx 1. Graph Equasions 2. Label 3. Determine how to slice 4. Set up dA 5. dA = height*dx 6. Get range a & b from intersections 7. Plug in and find area```

### Volume by Disk

 ```dV = A(x) dx V = ∫A(x)dx Volume = ∫Radius2 * Thickness V = ∫(pi(r)2) dx```

### Volume by Washer

 ```dV = A(x) dx V = ∫A(x) dx Volume = ∫[(pi r out2)-(pi r in2)] dx```

Slice Perpendicular to Axis of Rotation

### Volume by Shell

 ```dVolume = Circumference * dArea dV = (2 pi r) dArea V = ∫(2 pi r)(Area)dx 1. Write: dV = 2 pi r dA 2. Find dA(height dx) 3. Find Radius(x or y) 4. Plug in 5. Take integral```

Slice Parallel to Axis of Rotation

### Average Value of a Function

 ```Average Value = 1/b-a * ∫f(x) dx Symmetry: If f(x) is EVEN, then ∫f(x)dx from -a to a = 2∫f(x) from 0 to a If f(x) is ODD, then ∫f(x)dx from -a to a = 0```

### Important Integrals

 ∫c f(x) dx = c ∫f(x) dx ∫[f(x) + g(x)] dx = ∫f(x) dx + ∫g(x) dx ∫ 1/x dx = ln|x| + C ∫ex dx = ex + C ∫bx dx = (bx / lnb) + C

### Methods of Integration

 Method When to Use Example U-Substitution When a Polynomial is raised to a power > 1 ∫(3x + 5)5 Integration by Parts When U-Sub will not work ∫xex Trigonometric Integration Only Trig raised to powers ∫sin6x cos3xdx Trigonometric Substitution 3/2 powers or Sqrt(a2-x2) etc. dx/(x2Sqrt(25-x2))

### Integration by Parts

 ```Logarithmic Inverse trig Algebraic Trigonometric Exponential ∫u dv = u v - ∫v du 1. Write u v - ∫v du 2. Use LIATE to find u; the other term becomes dV 3. Setup u= dV= du= V= 4. Solve```

Cyclical Functions will need to be split and substituted.

### Trigonometric Integration

 ```Identities sin2t+cos2t = 1 sin2t = 1/2 [1-cos(2t)] cos2t = 1/2 [1+cos(2t)] Can use with U-Substitution```

Don’t change all of the trig to the same form.

### Trigonometric Integration

 ```Identities sin2t+cos2t = 1 sin2t = 1/2 [1-cos(2t)] cos2t = 1/2 [1+cos(2t)] Can use with U-Substitution```

Don’t change all of the trig to the same form.

### Trigonometric Substitution

 ```Pythag. Identities sin2 + cos2 = 1 1 + tan2 = sec2 1 + cot2 = csc2 1. Identify a and u 2. Sub in the trig 3. Manipulate to simplify 4. Get rid of trig with a triangle```

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