Calculus 2: Trigonometric substitution

Evaluate the integral $\displaystyle \int \frac{dx}{\sqrt{x^2 + 16}}$ using trigonometric substitution.

Evaluate the integral $\displaystyle \int \frac{x}{\sqrt{x^2 - 7}} \, dx$ using trigonometric substitution.

Evaluate the indefinite integral $\displaystyle \int \frac{1}{\sqrt{4-x^2}} \, dx$.

Evaluate the integral using trigonometric substitution.

Using the trigonometric substitution $x = a \cdot \sec(\theta)$, simplify the expression involving the square root $\sqrt{x^2 - a^2}$.

Evaluate the integral $\displaystyle \int \frac{x}{\sqrt{25 - x^2}} \, dx$ using trigonometric substitution.

Evaluate $\displaystyle \int \frac{\sqrt{2x^2 - 1}}{x} \, dx$ using trigonometric substitution.

Evaluate $\displaystyle \int \frac{\sqrt{4 - x^2}}{x^2} \, dx$ from $\sqrt{2}$ to 2 using trigonometric substitution.

Using trigonometric substitution, integrate the following expressions: $\sqrt{a^2 - x^2}$, $\sqrt{a^2 + x^2}$, and $\sqrt{x^2 - a^2}$.

Integrate $\frac{y^2}{(16-y^2)^{3/2}}$ with respect to $y$.

Integrate $\frac{\sqrt{x^2 + 36}}{9x^2}$ with respect to $x$.

Evaluate the definite integral $\displaystyle \int_{9}^{18/\sqrt{3}} \frac{dt}{t\sqrt{t^2 - 81}}$ using trigonometric substitution.

Find the area under the curve $y = \sqrt{1 - x^2}$ from $x = 0$ to $x = 1$ using trigonometric substitution.

Evaluate $\displaystyle \int_{0}^{\frac{1}{2}} \sqrt{1-x^2} \, dx$ using trigonometric substitution, where $x=\sin\theta$.

Perform a trigonometric substitution for evaluating the integral involving inverse substitution where $x=\frac{1}{2}u$.

Evaluate the integral using trigonometric substitution where $x = 3 \sin \theta$ for the expression involving $\sqrt{9 - x^2}$.

Use trigonometric substitution to solve the integral involving a square root: integrate from $-3$ to $3$ the square root of $9 - x^2$ $dx$.

Using trigonometric substitution, solve integrals that have integrals involving $a^2 - u^2$, $a^2 + u^2$, and $u^2 - a^2$ inside the radical.

Using trigonometric substitution, solve integrals involving $a^2 + u^2$ under the radical.

Integrate $\frac{x^3}{\sqrt{16-x^2}}$ using trigonometric substitution.