Calculus Examples

$\int \frac{\sin (20 t)}{\sin (10 t)} d t$

Step 1

Rewrite $\frac{\sin (20 t)}{\sin (10 t)}$ as a product.

$\frac{d}{d x} [\int \sin (20 t) \frac{1}{\sin (10 t)} d t]$

Step 2

Write $\sin (20 t)$ as a fraction with denominator $1$ .

$\frac{d}{d x} [\int \frac{\sin (20 t)}{1} \cdot \frac{1}{\sin (10 t)} d t]$

Step 3

Simplify.

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Step 3.1

Divide $\sin (20 t)$ by $1$ .

$\frac{d}{d x} [\int \sin (20 t) \frac{1}{\sin (10 t)} d t]$

Step 3.2

Convert from $\frac{1}{\sin (10 t)}$ to $\csc (10 t)$ .

$\frac{d}{d x} [\int \sin (20 t) \csc (10 t) d t]$

Step 4

Since $\int \sin (20 t) \csc (10 t) d t$ is constant with respect to $x$ , the derivative of $\int \sin (20 t) \csc (10 t) d t$ with respect to $x$ is $0$ .

$0$