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Use the result

[[math]] \int_1^2 x^n \; dx = \frac{2^{n+1} - 1}{n+1}, \quad n=0,1,2,\ldots , [[/math]]

and the analogous result at the beginning of Problem Exercise to evaluate

• [math]\int_1^2 (3x^2 - 2x + 1) \; dx[/math]
• [math]\int_0^2 x^2 \; dx[/math]
• [math]\int_0^2 (4x^3 - 3x + 2) \; dx[/math]
• [math]\int_0^2 (t^3 + t^2 + t) \; dt[/math].