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Model Paper 3 — Applied Maths STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceApplied MathsModel Paper 32 Marks
Question
Evaluate: $\int_{1}^{2}\left(4 x^{3}-5 x^{2}+6 x+9\right) d x$
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Answer

$\int_{1}^{2}\left(4 x^{3}-5 x^{2}+6 x+9\right) d x=\left[4 \cdot \frac{x^{4}}{4}-5 \cdot \frac{x^{3}}{3}+6 \cdot \frac{x^{2}}{2}+9 x\right]_{1}^{2}$
$=\left[x^{4}-\frac{5}{3} x^{3}+3 x^{2}+9 x\right]_{1}^{2}=\left(16-\frac{40}{3}+12+18\right)-\left(1-\frac{5}{3}+3+9\right)$
$=46-\frac{40}{3}-13+\frac{5}{3}=33-\frac{35}{3}=\frac{64}{3}$.

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