Arc Length Integral Setup

Particle Velocity from Acceleration

Volume of a Solid of Revolution

Volume Using the Shell Method

Area Between Curves With Respect to y

Determine the number c in the interval [1,3] that satisfies the Mean Value Theorem for Integration for $$f(x)=x^2$$. Solve the equation: $$\frac{1}{3-1}\int_{1}^{3} x^2 dx = c^2$$ for c.

Velocity From Acceleration

Volume with Rectangular Cross Sections

Volume by Rotation About a Horizontal Line

Area Between Two Curves

Solve for the derivative of the function $$f(x)= \cos(5*x^3)$$ using the chain rule.

Chain Rule with an Inverse Sine Function

A differentiable function $$f(x)$$ satisfies $$f(2)=5$$ and $$f'(2)=4$$. If its inverse function is $$g(x)$$, use the inverse function derivative formula to compute $$g'(5)$$.

Implicit Differentiation

Chain Rule Application Order

Implicit Differentiation Concepts

For the relation $$\sin(x+y)=x*y$$, use implicit differentiation to find an expression for $$\frac{dy}{dx}$$ in terms of x and y.

Implicit Differentiation

Given the equation $$x^2+y^2=25$$, use implicit differentiation to find $$\frac{dy}{dx}$$.

Applying the Chain Rule to Composite Functions