Unit Six: Integration and Accumulation of Change

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Last updated 10:28 PM on 12/8/22
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40 Terms

1
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Integral of cf(x)dx
c integral f(x)dx
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Integral from a to b f(x)dx
-(negative) integral from b to a f(x)dx
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integral from a to c f(x)dx
integral from a to b f(x)dx + integral from b to c f(x)dx
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integral from a to a f(x)dx
0
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integral from a to b -f(x)dx
-(negative) integral from a to b f(x)dx
6
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Integral of (f(x)+g(x))dx
integral f(x)dx + integral g(x)dx
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Fundamental Theorem of Calculus
∫ f(x) dx on interval a to b = F(b) - F(a)
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Integral from a to b of c
cx|(a to b)
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integral from a to b of cxˆn
cxˆ(n+1)/n+1 |(a to b)
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integral from a to b 1/xdx
ln|x| |(a to b)
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integral of sinx dx
-cosx + c
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integral of secˆ2x dx
tanx + c
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Integral of cscxcotx dx
-cscx + C
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integral of cosx dx
sinx + c
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integral of cscˆ2x dx
-cotx + c
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integral of secxtanx dx
secx + c
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integral of e^x dx
e^x + c
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integral of eˆ5x dx
1/5 eˆ(5x) + c
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Riemann Sum
lim n -> ∞ Σ k = 1 to n f(xk*) • Δx
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lim n -> ∞ Σ k = 1 to n f(xk*) • Δx
lim n -> ∞ Σ k = 1 to n f(a+k((b-a)/n)) • (b-a)/n
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xk*
a+kΔx
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Δx
(b-a)/n
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Fundamental theorem of calculus (derivative)
d/dx F(x)= d/dx integral from a to x f(t) dt = f(x)
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When dealing with fundamental theorem of calc. (derivative) and the x is different (such as xˆ2), use
Chain rule
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Displacement
Integrate velocity
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Integral from a to b of v(t) dt
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Total distance traveled
Integrate speed
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Integral from a to b of |v(t)| dt
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Displacement
How much you moved from starting position
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Acceleration
Derivative of velocity
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Position
Antiderivative of velocity
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Average value theorem
1/b-a integral from a to b of f(x) dx
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F(x) is inc. then LRAM will be an
Underapproximation (LRAM)
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F(x) is Dec. then LRAM will be an
Overestimate (LRAM)
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F(x) is inc. then RRAM will be an
Overestimate (RRAM)
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F(x) is Dec. then RRAM will be an
Underestimate (RRAM)
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F(x) is ccd. then MRAM will be an
Overestimate (MRAM)
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F(x) is ccu. then MRAM will be an
Underestimate (MRAM)
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F(x) is ccd. then TAM will be an
Underestimate (TAM)
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F(x) is ccu. then TAM will be an
Overestimate (TAM)