Integral Calculus Cheat Sheet - Web applying the fundamental theorem of calculus to the square root curve, f (x) = x^ {1/2} f (x) = x1/2, we look at the antiderivative, f (x) = \frac {2} {3} \cdot x^\frac {3} {2} f (x) = 32 ⋅x23 , and simply take f (1) − f (0) f (1)−f (0), where 0 0 and 1 1 are the boundaries of the interval [0,1] [0,1]. Divide [ab,] into n subintervals of width d x and choose * xi from each interval. Suppose fx( ) is continuous on [ab,]. Save a du x dx sin( ) ii. © 2005 paul dawkins integrals definitions definite integral: Then () (*) 1 lim i b a n i fxd xx æ• = • ú =â d. © 2005 paul dawkins integrals definitions definite integral: If the power of the sine is odd and positive: Then () (*) 1 lim i b a n i fxdxfxx fi¥ = ¥ ò =då. Divide [ab,] into n subintervals of width dx and choose * x i from each interval.
Divide [ab,] into n subintervals of width dx and choose * x i from each interval. Suppose fx( ) is continuous on [ab,]. © 2005 paul dawkins integrals definitions definite integral: Then () (*) 1 lim i b a n i fxdxfxx fi¥ = ¥ ò =då. If the power of the sine is odd and positive: Divide [ab,] into n subintervals of width d x and choose * xi from each interval. Integrals involving sec(x) and tan(x): © 2005 paul dawkins integrals definitions definite integral: Web applying the fundamental theorem of calculus to the square root curve, f (x) = x^ {1/2} f (x) = x1/2, we look at the antiderivative, f (x) = \frac {2} {3} \cdot x^\frac {3} {2} f (x) = 32 ⋅x23 , and simply take f (1) − f (0) f (1)−f (0), where 0 0 and 1 1 are the boundaries of the interval [0,1] [0,1]. Save a du x dx sin( ) ii. Then () (*) 1 lim i b a n i fxd xx æ• = • ú =â d. Integrals involving sin(x) and cos(x): Suppose fx( ) is continuous on [ab,]. Convert the remaining factors to cos( )x (using sin 1 cos22x x.) 1.