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MATHEMATICS

JAMB 2002 - Question 10

Mathematics 2002 JAMB Past Questions - Question 10: Evaluate integral sin3x dx

Evaluate integral sin3x dx

A: 2/3 cos 3x+c

B: 1/3 cos 3x+c

C: -1/3 cos 3x

D: -2/3 cos 3x+c

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Correct Answer

Explanation

To evaluate the integral ∫ sin(3x) dx, we can use the substitution method.Let's substitute u = 3x, then du = 3 dx. Rearranging, we have dx = du/3.Now, we can rewrite the integral in terms of u:∫ sin(3x) dx = ∫ sin(u) (du/3)Pulling out the constant 1/3:(1/3) ∫ sin(u) duIntegrating sin(u) with respect to u gives us -cos(u):(1/3) (-cos(u)) + CSubstituting back u = 3x:(1/3) (-cos(3x)) + CTherefore, the evaluated integral of sin(3x) dx is (-1/3)cos(3x) + C, where C is the constant of integration.