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# Calc 142

### Math shiz

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

What is the definite integral for Calculus? | Given a function that is continuous on the interval [a,b] we divide the interval into n subintervals of equal width, , and from each interval choose a point, x*i. Then the definite integral of f(x) from a to b is |

What is the Fundamental Theorem of Calculus PT 1? | Let f be a continuous function on a defined interval [a,b]: If A(x) is the function A(x) on a to x integral f(t)dt, for all x on [a,b] then A'(x) = f(x) for all x on [a,b]. |

What is the Fundamental Theorem of Calculus PT 2? | Let f be continuous function on a defined interval [a,b]: If F(x) is any antiderivative of f(x), then the integral from a to b f(x)dx = F(b)-F(a). |

Half-angle formula? | cos^2(a)= 1/2(1+cos(2a)) sin^2(a)= 1/2(1-cons(2a)) |

a^2-x^2, a^2+x^2, x^2+a^2? | (x = asin(theta), 1-sin^2theta = cos^2theta) (x = atan(theta), 1 + tan^2(theta) = sec^2(theta)), (x = asec(theta), sec^2(theta) - 1 = tan^2(theta)). |

sin(2a) = ? | 2sin(a)cos(a) |

cos(2a) = ? | 1 - 2sin^2(a) |

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