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If $y = x(x^4 + x + 1)$ , evaluate \(\int \limits_{0} ^{1}&...

If $y = x(x^4 + x + 1)$ , evaluate $\int \limits_{0} ^{1} y \mathrm d x$ .

A.

$\frac{11}{12}$

B.

1

C.

$\frac{5}{6}$

D.

zero

View answer & explanation

Correct answer is B

$y = x(x^{4} + x + 1) = x^{5} + x^{2} + x$

$\int \limits_{0} ^{1} (x^{5} + x^{2} + x) \mathrm d x = \frac{x^{6}}{6} + \frac{x^{3}}{3} + \frac{x^{2}}{2}$

= $[\frac{x^{6}}{6} + \frac{x^{3}}{3} + \frac{x^{2}}{2}]_{0} ^{1}$

= $\frac{1}{6} + \frac{1}{3} + \frac{1}{2}$

= $1$

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