Calculus 1

Approximate $f(x) = \sqrt[3]{x}$ at $x = 26$

Let $f(x) = \sqrt{x}$ at $x = 4$ and $\Delta{x} = 0.02$

Find $dx$, $dy$, $\Delta{y}$

Evaluate the following indefinite integral

$\displaystyle\int{3x^6} dx$

Evaluate the following integral

$\displaystyle\int (3x + 5x^2) \ dx$

Let $f^\prime(x) = 2x$ what is the antiderivative, $f(x)$ ?

Evaluate the indefinite integral below

$\displaystyle\int (x^3 + 2x - 1) \ dx$

Evaluate the following integral

$\displaystyle\int (x + 1) \sqrt{2x + x^2} \ dx$

Evaluate $\displaystyle\int x^5 \sqrt{1 + x^2} \ dx$

Evaluate the integral

$\displaystyle\int_0^2 (2x - 2x^2) \ dx$

Compute the area between $y = \sin{x}$ and $y = \cos{x}$ and the interval $[\frac{\pi}{4}, \frac{5\pi}{4}]$

Use the disk method to find the volume of the solid of rotation by rotating the bounded area around the y-axis

$y = 2x^2$, $y = 0$, $x = 2$