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JAMB Mathematics 2010 Paper

Question : 17

Total: 49

Find ∫(sin x + 2)dx

Solution:

Concept:

The integral of a sum is the sum of the integrals of each term.

Explanation:

Write the integral as two separate integrals:

\int(\sin x + 2)\,dx = \int \sin x\,dx + \int 2\,dx

Integrate each term:

\int \sin x\,dx = -\cos x

\int 2\,dx = 2x

Add the constant of integration

K

-\cos x + 2x + K

Check by differentiating:

\frac{d}{dx}(-\cos x + 2x + K) = \sin x + 2

, which matches the integrand.

Answer:

Option D:

-\cos x + 2x + K

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