Posts in Learn math
U-substitution to solve definite integrals

U-substitution in definite integrals is just like substitution in indefinite integrals except that, since the variable is changed, the limits of integration must be changed as well. If you don’t change the limits of integration, then you’ll need to back-substitute for the original variable at the end.

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Learn mathKrista King
Polar coordinates vs. rectangular coordinates

Any point in the coordinate plane can be expressed in both rectangular coordinates and polar coordinates. Instead of moving out from the origin using horizontal and vertical lines, like we would with rectangular coordinates, in polar coordinates we instead pick the angle, which is the direction, and then move out from the origin a certain distance.

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Learn mathKrista King
Vertical angles as congruent angles

Vertical angles are angles in opposite corners of intersecting lines. So vertical angles always share the same vertex, or corner point of the angle. They’re a special angle pair because their measures are always equal to one another, which means that vertical angles are congruent angles.

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Learn mathKrista King
Theorem of Pappus to find volume using the centroid

The Theorem of Pappus tells us that the volume of a three-dimensional solid object that’s created by rotating a two-dimensional shape around an axis is given by V=Ad. V is the volume of the three-dimensional object, A is the area of the two-dimensional figure being revolved, and d is the distance traveled by the centroid of the two-dimensional figure.

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Calculating absolute values

The absolute value operation turns any value inside it into its distance from the origin, essentially turning both positive and negative numbers into only positive numbers. Always calculate the value inside the absolute value first, then apply the absolute value last.

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Learn mathKrista King
Number sets in the real number system

The vast majority of the numbers you’ll use in most math classes are called real numbers, and the whole universe of real numbers is what makes up the Real Number System. Let’s start with a diagram.

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