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Find the area bounded by the curve y = 3x $^2$ - 2x + ...

Find the area bounded by the curve y = 3x $^2$ - 2x + 1, the ordinates x = 1 and x = 3 and the x-axis.

A.

24

B.

22

C.

21

D.

20

View answer & explanation

Correct answer is D

$\frac{\mathrm d y}{\mathrm d x} = 3x^{2} - 2x + 1$

$y = \int_{1} ^{3} (3x^{2} - 2x + 1) \mathrm d x$

$y = [x^{3} - x^{2} + x]_{1} ^{3}$

= $[3^{3} - 3^{2} + 3] - [1^{3} - 1^{2} + 1]$

= $21 - 1 = 20$

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