Question

Evaluate the following indefinite integral: ∫(10sin(x) - 2cos(x))dx = ______ + C

a) 10sin(x) + 2cos(x)
b) -10cos(x) - 2sin(x)
c) -10cos(x) + 2sin(x)
d) 10sin(x) - 2cos(x)

Answer 1

The indefinite integral ∫(10sin(x) - 2cos(x))dx is evaluated by using the antiderivatives of sine and cosine functions, resulting in the answer -10cos(x) - 2sin(x) + C.

Step-by-step explanation:

The student has asked to evaluate the following indefinite integral: ∫(10sin(x) - 2cos(x))dx. To do this, we recall the basic antiderivatives of sine and cosine functions. The integral of sin(x) with respect to x is -cos(x), and the integral of cos(x) with respect to x is sin(x). Therefore, we apply these rules to the integral:

• ∫10sin(x)dx = 10(-cos(x)) = -10cos(x)
• ∫(-2cos(x))dx = -2sin(x)

Combining these results, we obtain the integral of the given function as:

∫(10sin(x) - 2cos(x))dx = -10cos(x) - 2sin(x) + C

So, the correct answer is b) -10cos(x) - 2sin(x) + C.