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MATHEMATICS

JAMB 2016 - Question 12

Mathematics 2016 JAMB Past Questions - Question 12: Evaluate ∫(cos 4x+sin3x)dx.

Evaluate ∫(cos 4x+sin3x)dx.

A: sin4x-cos3x+k

B: sin4x+cos3x+k

C: 1/4sin4x-1/3cos3x+k

D: 1/4sin4x+1/3cos3x+k

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Correct Answer

Explanation

(cos 4x +sin3x)dx= 1/4 sin 4x - 1/3 cos 3x +kTo evaluate the integral of cos(4x) + sin(3x) with respect to x, you can integrate each term separately.The integral of cos(4x) with respect to x is (1/4)sin(4x) + C, where C is the constant of integration.The integral of sin(3x) with respect to x is (-1/3)cos(3x) + C, where C is the constant of integration.Therefore, the integral of cos(4x) + sin(3x) with respect to x is:(1/4)sin(4x) - (1/3)cos(3x) + CSo, ∫(cos 4x+sin3x)dx = (1/4)sin(4x) - (1/3)cos(3x) + C