34 Calculus Tutorials

These Calculus tutorials are written by experienced educators, all of whom also offer private tutoring lessons. Get the Calculus help you need, whether through these tutorials or through private tutoring lessons.

Trigonometric Integrals

Still in integration where our objective is to find the anti derivative of a certain function, in this case trigononetric functions. But first we will be dealing with simple trigonometric integrals.

Integration by Parts

The integration by parts formula S udv = uv – S vdu is derived from the product rule of differentiation d (uv) = vdu + udv. From the derivative form we will be making the function or equation back to its original function though it is in product form. I will be giving example(s) how…

Why is the Integral an Anti-derivative?

We will use the following definitions: Anti-Derivative : The anti-derivative of a function f is a function F such that F' = f. Integral (area definition) : The integral of \int_a^b f(x) dx of f is the area under the curve f(x) from x=a to x=b. Let us define the area under the curve f

Logarithmic Differentiation

You need to use Logarithmic Differentiation when you want to find the derivative of a function that is in the (x^x) form. You start out by equating y to any function that is (x^x). You then apply logarithmic rules to the function by encasing “y” with ln and bringing the power of “x” down in…

Differential Equations

Handling of Materials Suppose that we have a tank containing water. Suppose also that we have 2 pumps — one pump can drain the tank in 6 hours, and the other can drain the tank in 5 hours. How long will it take to drain the tank with both pumps running? Since one pump can…

Derivatives and Integrals

Fine a derivative and an integral that are the same.

Different Differentiation Rules

Any problem that can be solved with the quotient rule can also be solved with the product rule and chain rule.

Product Rule Differentiation (Single Variable)

The product rule is used when you are finding the derivative of a function that has one dependent variable expression multiplied by another dependent variable expression. Compare this function: f(x) = x2 + 2×5 …with this function: g(x) = x4cos(x) Function g(x) can be thought of as two separate functions multiplied together: h(x) = x4…

finding domain of a complex function

If in a problem you are required to find the domain of a function which is the sum of two or more functions then the domain of the combined function will be the union of domains of individual function.

Quotient Rule (Single Variable)

The quotient rule is when a larger function is composed of two differentiable functions divided by one another like so: