MATHEMATICS

JAMB 2007 - Question 11

Mathematics 2007 JAMB Past Questions - Question 11: Integrate x² - √x/x with respect to x

Integrate x² - √x/x with respect to x
A:
B:
C:
D:
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Correct Answer

D

Explanation

ʃ (x²- √x/x )dx = ʃ (x² /x - x¹⁄₂ )dx= ʃ (x-x- ¹⁄₂ )dx = x²/2 - x¹⁄₂ /¹⁄₂ + c = x² /2 – 2 √x + kTo integrate the expression ∫(x² - √x)/x dx, we can split it into two separate integrals:∫(x²/x) dx - ∫(√x/x) dxSimplifying each integral:∫x dx - ∫(√x/x) dxIntegrating each term:∫x dx = (1/2)x² + C1For the second integral, we can rewrite it as:∫(√x/x) dx = ∫x^(-1/2) dxUsing the power rule of integration:∫x^(-1/2) dx = 2x^(1/2) + C2Combining the results:∫(x² - √x)/x dx = (1/2)x² - 2√x + CWhere C = C1 + C2 is the constant of integration.