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# Calc 113 1

### Calculus Integration part 1

Question | Answer |
---|---|

Sin(x)Cos(y) | 1/2(sin(x-y) + sin(x+y)) |

sin(x)sin(y) | 1/2(cos(x-y) - cos(x+y)) |

cos(x)cos(y) | 1/2(cos(x-y) + cos(x+y)) |

sin^2(x) | 1-cos(2x)/2 |

cos^2(x) | 1+cos(2x)/2 |

(a^2-x^2)^1/2 subst? | x=asin(t) |

Sin(x)Cos(y) | 1/2(sin(x-y) + sin(x+y)) |

(a^2-x^2)^1/2 which identity do you use? | 1-sin^2(t)=cos^2(t) |

sin(x)sin(y) | 1/2(cos(x-y) - cos(x+y)) |

(a^2+x^2)^1/2 which identity do you use? | 1+tan^2(t)=sec^2(t) |

cos(x)cos(y) | 1/2(cos(x-y) + cos(x+y)) |

sin^2(x) | 1-cos(2x)/2 |

cos^2(x) | 1+cos(2x)/2 |

(x^2-a^2)^1/2 which identity do you use? | sec^2(t)-1=tan^2(t) |

(a^2-x^2)^1/2 subst? | x=asin(t) |

Intergral f'(x)g(x)dx = | f(x)g(x)-integral f(x)g'(x)dx |

(a^2-x^2)^1/2 which identity do you use? | 1-sin^2(t)=cos^2(t) |

Shell Method | V=2(pi)rh(dr) V=(circumference)(height)(thickness) integral 2(pi)x(f(x))dx |

(a^2+x^2)^1/2 subst? | x=atan(t) |

Volumes formula | V=integral A(x)dx A(x)=area |

(a^2+x^2)^1/2 which identity do you use? | 1+tan^2(t)=sec^2(t) |

Washer Method | V=integral (pi)r^2-(pi)r^2dx V=integral (pi)(outer radius)^2 - (pi)(inner radius)^2 dx |

(x^2-a^2)^1/2 subst? | x=asec(t) |

Shell Method choosing variable of integral | Variable of the integral should be in the same direction as the axis of rotation x=0 is dx y=0 is dy |

(x^2-a^2)^1/2 which identity do you use? | sec^2(t)-1=tan^2(t) |

Washer Method choosing variable of integral | variable of integral should be going the opposite direction of the axis of rotation(but can be either) x=0 is dy y=0 is dx |

Intergral f'(x)g(x)dx = | Intergral f'(x)g(x)dx = f(x)g(x)-integral f(x)g'(x)dx |

Work = ? | W=fd or W=mgd work=force*distance or work=(mass*gravity)*distance |

Shell Method | V=2(pi)rh(dr) V=(circumference)(height)(thickness) integral 2(pi)x(f(x))dx |

Work = ? (integral) | W=integral f*dx |

Volumes formula | V=integral A(x)dx A(x)=area |

Hook's Law | F=kd Force=(hook's constant)(distance stretched from natural length) |

Washer Method | V=integral (pi)r^2-(pi)r^2dx V=integral (pi)(outer radius)^2 - (pi)(inner radius)^2 dx |

Work = (integral)(Hook's Law) | W= integral k*x*dx |

Shell Method choosing variable of integral | Variable of the integral should be in the same direction as the axis of rotation x=0 is dx y=0 is dy |

Average value | |

Washer Method choosing variable of integral | variable of integral should be going the opposite direction of the axis of rotation(but can be either) x=0 is dy y=0 is dx |

Work = ? | W=fd or W=mgd work=force*distance or work=(mass*gravity)*distance |

Work = ? (integral) | W=integral f*dx |

Hook's Law | F=kd Force=(hook's constant)(distance stretched from natural length) |

Work = (integral)(Hook's Law) | W= integral k*x*dx |

Average value of a function | 1/(b-a) intergral f(x)dx |

Work = (pumping) | W=integral (distance)(density)(area)dx Work=integral (distance cross section will move)(density)(area of cross section)(dx or dy) |

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