Simplifying the process: Evaluating the Integral of sin(x) using the Substitution Method

∫sinxdx

To evaluate the integral ∫sin(x)dx, you can use the substitution method

To evaluate the integral ∫sin(x)dx, you can use the substitution method.

Let’s start by letting u = cos(x):

Differentiating both sides with respect to x, we get du = -sin(x)dx.

Rearranging the equation, we have -du = sin(x)dx.

Substituting these values into the integral, we get:

∫sin(x)dx = ∫-du

Since -du is a constant with respect to x, we can pull it out of the integral:

∫-du = -∫du

∫-du simplifies to -u. So, the final answer is:

∫sin(x)dx = -cos(x) + C

Where C is the constant of integration.

More Answers: