Fundamental Theorem of Calculus Part I : If f ( x ) is continuous on [ a , b ] then x ) = ò a

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Let u=f(x) (can be more than one variable). Determine: f(x) du= dx and solve for dx dx. Then, if a definite integral, substitute the bounds for u=f(x) at each bounds Solve the integral using u.

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To find the maximum and minimum values of a function y f (x ) , locate. the points where f (x ) is zero or where f (x ) fails to ′ ′ exist. the end points, if any, on the domain of f (x ) .

Suppose that f ( x ) is continuous on [a, b] and let M be any number between f ( a ) and f ( b ) . Then there exists a number c such that a < c < b and f ( c ) = M . If y = f ( x ) then all of the following are …

Partial list of continuous functions and the values of x for which they are continuous. Polynomials for all x. 7. cos x and sin x for all x. Rational function, except for x’s that give division by zero. 8. tan x and …

022 This cheat sheet will be included in th. midterm. You do NOT have to memorize these formulas. However, make sure th. t you understand and know how to apply ALL of them!!! If a constant is not …

Fundamental Theorem of Calculus [ ] Part I : If f ( x ) is continuous on a , b then ( x x ) = ò a