Evaluate₀¹ x²(x³+2)³

Correct Answer is : 6512\;65/121265

Correct Answer is : 6512\;65/121265

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WAEC Further Mathematics 2022 Paper

Question : 15

Total: 45

Evaluate

\int\limits_{0}^{1} x^2(x^3+2)^3

Solution:

Concept:

Use substitution to simplify the integral into a basic power rule integration.

Explanation:

Let

u = x^3 + 2

Then

du = 3x^2 \, dx

, so

x^2 \, dx = \frac{du}{3}

Change the limits: when

x = 0

u = 2

; when

x = 1

u = 3

The integral becomes

\int_{2}^{3} \frac{u^3}{3} \, du

Integrate:

\frac{1}{3} \cdot \frac{u^4}{4} = \frac{u^4}{12}

Apply limits:

\frac{1}{12}[3^4 - 2^4] = \frac{1}{12}[81 - 16]

Simplify:

\frac{65}{12}

Answer:

\frac{65}{12}

, which is option B.

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