∫(sinx)dx
To find the integral of sin(x), we can use the integration technique known as integration by parts
To find the integral of sin(x), we can use the integration technique known as integration by parts. The formula for integration by parts is:
∫(u * v)dx = u * ∫vdx – ∫(u’ * ∫vdx)dx
Let’s assign u = sin(x) and dv = dx. Therefore, du = cos(x)dx and v = x.
Using the formula for integration by parts, the integral of sin(x) can be written as:
∫(sinx)dx = sin(x) * ∫dx – ∫(cosx * ∫dx)dx
Simplifying further:
∫(sinx)dx = sin(x) * x – ∫(cosx)dx
Now, we can integrate ∫(cosx)dx using the formula ∫cos(x)dx = sin(x) + C, where C is the constant of integration. Applying this formula, we get:
∫(sinx)dx = sin(x) * x – sin(x) + C
Therefore, the integral of sin(x) is equal to sin(x) * x – sin(x) + C, where C is the constant of integration.
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