Integral Calculus Unit One Review

Contains Derivatives, Integrals, Formulas, and Terms to know

Derivative:

sin(x)

cos(x)

Derivative:

cos(x)

-sin(x)

Integral:

cos(x)dx

sin(x)+c

Integral:

sin(x)dx

-cos(x)+c

Integral:

e^x

e^x+c

Integral:

1/(x²+b²)

1/b*arc-tan(x)+c

Product rule

An integral which contains infinity in its limits or has a discontinuity within the limits.

Improper Integral

Divergent

Convergent

Divergent

Convergent

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Comparison Test

Technique to use in this case:

$$\int^{}\!g^{\prime}\left(x\right)f\left(g\left(x\right)\right)\,dx$$

U substitution

Integration by Parts

Trapezoid Rule

Which Trend?

Concave Up = Overestimate

Concave Down = Underestimate

Trapezoid

Which Trend?

Concave Up = Underestimate

Concave Down = Overestimate

Midpoint

Which Trend?

Increasing = Underestimate

Decreasing = Overestimate

Left Endpoint

Which Trend?

Increasing = Overestimate

Decreasing = Underestimate

Right Endpoint

Washer Method

Disk Method

Arc Length

Center of Mass

Total Moment/Total Mass

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Partial Fractions