Question on: JAMB Mathematics - 1994
Evaluate \(\int^{1}_{-1}\)(2x + 1)2dx
A
3\(\frac{2}{3}\)
B
4
C
4\(\frac{1}{3}\)
D
4\(\frac{2}{3}\)
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Correct Option: D
\(\int^{1}_{-1}\)(2x + 1)2dx
= \(\int^{1}_{-1}\)(4x2 + 4x + 1)dx
= \(\int^{1}_{-1}\)[\(\frac{4x^3}{3}\) + 2x2 + c]
= [\(\frac{4}{3}\) + 3 + c] - [4 + \(\frac{1}{3}\) + c]
= \(\frac{8}{3}\) + 3 + -1 - C
= \(\frac{8}{3}\) + 2
= \(\frac{14}{3}\)
= \(\frac{42}{3}\)
= \(\int^{1}_{-1}\)(4x2 + 4x + 1)dx
= \(\int^{1}_{-1}\)[\(\frac{4x^3}{3}\) + 2x2 + c]
= [\(\frac{4}{3}\) + 3 + c] - [4 + \(\frac{1}{3}\) + c]
= \(\frac{8}{3}\) + 3 + -1 - C
= \(\frac{8}{3}\) + 2
= \(\frac{14}{3}\)
= \(\frac{42}{3}\)
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