Clearly state the quantity of the three sides in the right triangle you are going to use, and
mark them at the graph;
then make substitution and solve the integral.
Transcribed Image Text:### Educational Content
**Mathematical Expression:**
b. \(\int \sqrt{16 - x^2} \, dx\)
**Diagram Explanation:**
The image includes a right triangle. It is labeled with an angle \(\theta\). The sides of the triangle are not labeled with specific lengths or variables in the image.
This integral and triangle suggest the application of a trigonometric substitution method, which is frequently used in calculus for integrals involving roots of the form \(\sqrt{a^2 - x^2}\). The angle \(\theta\) in the triangle can be used to define a relationship between the variables using trigonometric identities.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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