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JAMB 2010 · UTME · Q43

Evaluate ∫02(x3+x2) dx\displaystyle\int_0^2 (x^3 + x^2)\,dx.

Worked solution (try it first)
  1. Integrate: [x44+x33]02\left[\frac{x^4}{4} + \frac{x^3}{3}\right]_0^2.
  2. At x=2x = 2: 164+83=4+83\frac{16}{4} + \frac83 = 4 + \frac83
    =623= 6\frac23.
  3. At x=0x = 0 it is 0.
  4. So the integral is 6236\frac23, option B.

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