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tags: Pure Mathmatics
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# Integration
## (c) Dr. Zhou, UK :uk:


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1. $\int {y}\;dx=\frac{2X^4}{4}+\frac{5X^3}{3}-\frac{7X^2}{2}+10x+c=\frac{X^4}{2}+\frac{5X^3}{3}-\frac{7X^2}{2}+10x+c$

2. $\int{(3x^2+7x-2)}\;dx=X^3+\frac{7X^2}{2}-2x＋c$

3. $\int(x+4)(x-3)~dx=\int(x^2+x-12)\;dx=\frac{X^3}{3}+\frac{X^2}{2}-12x+c$
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$\int_{1}^{3}(x+4)(x-3)\;dx=\int_{1}^{3}(x^2+x-12)~dx=\left[\frac{x^3}{3}+\frac{x^2}{2}-12x+c\right]_{1}^{3}$
$=\left(\frac{3^3}{3}+\frac{3^2}{2}-12\times3\right)-\left(\frac{1^3}{3}+\frac{1^2}{2}-12\times1\right)=-\frac{45}{2}+\frac{67}{6}=-\frac{34}{3}$
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