MATHEMATICS

JAMB 2001 - Question 38

Mathematics 2001 JAMB Past Questions - Question 38: Evaluate ∫2(2x−3)23dx∫2(2x−3)^2/3dx

Evaluate ∫2(2x−3)23dx∫2(2x−3)^2/3dx
A:
B:
C:
D:
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Correct Answer

D

Explanation

To evaluate the integral ∫ 2(2x - 3)^(2/3) dx, we can use the substitution method.Let's make the substitution:u = 2x - 3Differentiating both sides with respect to x, we get:du/dx = 2Solving for dx, we have:dx = du/2Now, let's substitute these values into the integral:∫ 2(2x - 3)^(2/3) dx = ∫ 2u^(2/3) * (du/2)Simplifying, we have:∫ u^(2/3) duUsing the power rule for integration, we add 1 to the exponent and divide by the new exponent:∫ u^(2/3) du = (3/5) * u^(5/3) + CSubstituting back u = 2x - 3, we have:(3/5) * (2x - 3)^(5/3) + CTherefore, the evaluated integral is:(3/5) * (2x - 3)^(5/3) + C, where C is the constant of integration.