<s>[INST] function - area under the curve Trying to find area under the curve for the function $f(x)= 4x^3 + 3x^2 - x + 1$ on the interval $[1,2]$.     
My answer is:                       
$$\int_{1}^2 4x^3 + 3x^2 - x + 1 dx = \left[\frac{4x^4}{4} + \frac{3x^3}{3} – \frac{x^2}{2} + x + c\right]_1^2$$
$$\left[\frac{4.2^4}{4} + \frac{3.2^3}{3} – 2 + 2\right] – \left[\frac{4.1}{4} + 1 – \frac{1}{2} + 1\right] = 24 – 2.5 = 21.5$$
Is this correct? Thanks
 [/INST] Yes, you are correct.
Suggestion: To calculate faster, you may write down the simplest form before substituting the numbers.
e.g. change (4x^4)/4 to x^4.
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