Evaluate-1-1-0-x-2-x-1-dx-2-1-5-x-1-1-x-2-dx-

Question Number 32688 by Rio Mike last updated on 31/Mar/18

Evaluate

1) \int_{- 1}^{0} (x^{2} + x 1) dx

2) \int_{1}^{5} (x - 1 + \frac{1}{x^{2}}) dx

Answered by Joel578 last updated on 31/Mar/18

(1)

I = \int_{- 1}^{0} x^{2} + x + 1 d x

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

= (0) - (- \frac{1}{3} + \frac{1}{2} - 1)

= \dots

(2)

I = \int_{1}^{5} x - 1 + \frac{1}{x^{2}} d x

= {[\frac{1}{2} x^{2} - x - \frac{1}{x}]}_{1}^{5}

= (\frac{25}{2} - 5 - \frac{1}{5}) - (\frac{1}{2} - 1 - 1)

= \dots

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