Definite Integration
Integration of trigonometric functions
Grade Class 12
Question:
Suppose $J = \int \frac{\sin^2 x + \sin x}{1 + \sin x + \cos x} dx$ and $K = \int \frac{\cos^2 x + \cos x}{1 + \sin x + \cos x} dx$. If $C$ is an arbitrary constant of integration then which of the following is/are correct?
$J = \frac{1}{2} (x - \sin x + \cos x) + C$
$J = K - (\sin x + \cos x) + C$
$J = x - K + C$
$K = \frac{1}{2} (x - \sin x + \cos x) + C$
Step-by-Step Solution
Key Concept: Properties of integrals and trigonometric identities
Calculate J+K and J-K to simplify the expressions.
Correct Answer: B,C