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# System prepended metadata

title: Integration
tags: [Pure Mathmatics]

---

---
tags: Pure Mathmatics
---

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


![](https://i.imgur.com/UGB5QVt.png)



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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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![](https://i.imgur.com/6hTqguR.png)
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![](https://i.imgur.com/ys4XafE.jpg)
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![](https://i.imgur.com/9f4RPC5.png)
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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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![](https://i.imgur.com/OdUqWk9.png)
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![](https://i.imgur.com/LNsbodm.jpg)

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![](https://i.imgur.com/PV3CzQk.png)
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![](https://i.imgur.com/UhBLVJc.jpg)

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