Question Detail

Option B states that the indefinite integral of the derivative of a function f'(x) is the function f(x) (plus an arbitrary constant of integration, which is implied in indefinite integrals). This is a direct consequence of the Fundamental Theorem of Calculus. Let's examine other options:

• Option A: ∫e³x dx = (1/3)e³x + C, not 3e³x.
• Options C and D are identical. The derivative of cosec²x is d/dx[(cosec x)²] = 2(cosec x)(-cosec x cot x) = -2cosec²x cot x, which is not −(1/2)cosec x cot x.

Therefore, option B is the only correct statement.