What is the result of the integral ∫ (sin(x) + cos(x)) dx?

What is the result of the integral ∫ (sin(x) + cos(x)) dx?

• A. -cos(x) + sin(x) + C
• B. sin(x) - cos(x) + C
• C. cos(x) + sin(x) + C
• D. -sin(x) - cos(x) + C

Answer: (A)

To solve the integral ∫(sin(x) + cos(x))dx, we can break it down into two separate integrals: 1. The integral of sin(x) with respect to x is -cos(x). 2. The integral of cos(x) with respect to x is sin(x). Putting these results together, we have: ∫(sin(x) + cos(x))dx = ∫sin(x)dx + ∫cos(x)dx = -cos(x) + sin(x) + C Here, C is the constant of integration that arises because we are finding an indefinite integral. Therefore, the correct answer is the expression -cos(x) + sin(x) + C which accurately represents the outcome of the integration process.

To solve the integral ∫(sin(x) + cos(x))dx, we can break it down into two separate integrals:

1. The integral of sin(x) with respect to x is -cos(x).

2. The integral of cos(x) with respect to x is sin(x).

Putting these results together, we have:

∫(sin(x) + cos(x))dx = ∫sin(x)dx + ∫cos(x)dx

= -cos(x) + sin(x) + C

Here, C is the constant of integration that arises because we are finding an indefinite integral.

Therefore, the correct answer is the expression -cos(x) + sin(x) + C which accurately represents the outcome of the integration process.