Calculus 2

Evaluate $\int x \, sin(x) \, dx$

Evaluate $\int x^2 \, cos(x) \, dx$

Find the area enclosed by $x^2 + y^2 = r^2$.

Integrate $\frac{\sqrt{9-x^2}}{x^2} \, dx$ using trigonometric substitution.

Integrate $\frac{1}{x^2 \sqrt{x^2 + 4}} \, dx$ using trigonometric substitution.

Simplify and integrate the expression $(x^2 + 9)^{3/2}$ using trigonometric substitution where $x = 3\tan(\theta)$.

Evaluate the integral $\displaystyle \int \frac{dt}{t^2 + 9}$ using trigonometric substitution.

Integrate $1 \over \sqrt{a^2 - x^2}$.

Integrate the square root of $2-x^2$ over $x^2$.

Integrate the square root of $1 - 4x^2$.

Integrate $\displaystyle \frac{1}{x \sqrt{9-x^2}}$.

Integrate $\frac{\sqrt{4-x^2}}{x^2}$ using trigonometric substitution.

Find the indefinite integral of $\displaystyle \int \frac{x^3}{\sqrt{x^2 + 9}} \, dx$ using trigonometric substitution.

Perform the substitution $u = x + 1$ and express the integral $\displaystyle \int \sqrt{1 - (x + 1)^2}^5 \, dx$ in terms of $u$.

Perform the trigonometric substitution for the integral involving $\sqrt{1 + x^2}$.

Using a triangle, identify the trigonometric substitution for evaluating the integral involving $\sqrt{9 - x^2}$ and carry out the integration.

Find the integral of the function from $1$ to $3$ for $\frac{1}{(\sqrt{1 + x^2})^3}$ using trigonometric substitution and outline the process.

Perform the trigonometric substitution for the integral involving $\sqrt{x^2 - 4}$.

Using a triangle, identify the trigonometric substitution for the problem involving $x = 2 \theta$ and integrate.

Complete the square for the expression $x^2 - 2x + 3$ and rewrite it in the form $a - b^2$.