Mathematics 2015 JAMB Past Questions - Question 29: Evaluate ∫ sin 4xdx .

Correct Answer

B

Explanation

∫ sin4xdx=-cos4x+C /4To evaluate the integral of sin(4x) with respect to x, we can use the reverse chain rule, which states that the integral of sin(u) du is equal to -cos(u) + C, where C is the constant of integration.In this case, we have sin(4x), so we can let u = 4x. Then, du/dx = 4, which means du = 4dx. Solving for dx, we get dx = du/4.Substituting u = 4x and dx = du/4, the integral becomes:∫ sin(4x) dx = ∫ sin(u) * (1/4) du              = (1/4) * ∫ sin(u) du              = -(1/4) * cos(u) + C              = -(1/4) * cos(4x) + CSo, the result of the integral of sin(4x) with respect to x is -(1/4) * cos(4x) + C, where C is the constant of integration.To evaluate the integral of sin(4x) with respect to x, we can use the following steps:Let's use the substitution method. We can let u = 4x, then du = 4dx, which gives us dx = du/4.Substituting u = 4x and dx = du/4, the integral becomes:∫ sin(4x) dx = (1/4) ∫ sin(u) duThe integral of sin(u) with respect to u is -cos(u), so:(1/4) ∫ sin(u) du = -(1/4) cos(u) + CSubstituting back u = 4x, we get:-(1/4) cos(4x) + CTherefore, the result of the integral of sin(4x) with respect to x is -(1/4) cos(4x) + C, where C is the constant of integration.