INTEGRAL

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න 𝐷𝑋 න 𝑓(𝑥) 𝐷𝑋
INTEGRAL
REPRESENTAÇÃO
න 𝐷𝑋 න 𝑓(𝑥) 𝐷𝑋
INTEGRAL
REPRESENTAÇÃO
Funções
න24𝑥3𝑑𝑥 − න28𝑥3𝑑𝑥 − න3𝑥2𝑑𝑥 + න4 𝑑𝑥
න24𝑥3 − 28𝑥3 − 3𝑥2 + 4 𝑑𝑥
24න𝑥3𝑑𝑥 − 28න𝑥3𝑑𝑥 − 3න𝑥2𝑑𝑥 + 4න 𝑑𝑥
= 
24𝑥3+1
3+1
= 
24𝑥4
4
= 
24𝑥4
4
= 
6𝑥4
1
= 6𝑥4
= 
−28𝑥3+1
3+1
= 
−28𝑥4
4
= 
−28𝑥4
4
= 
−7𝑥4
1
= −7𝑥4
= 
−3𝑥2+1
2+1
= 
−3𝑥3
3
= 
−3𝑥3
3
= 
−𝑥3
1
= −𝑥3
= 4. 𝑥 + 𝑐 = 4𝑥 + 𝑐
𝑓 𝑥 = 6𝑥4- 7𝑥4 − 𝑥3+ 4𝑥 + 8
𝑓′ 𝑥 = 24𝑥3- 28𝑥3 − 3𝑥2+ 4
න28𝑥3 − 32𝑥3 − 9𝑥2 + 7𝑑𝑥
න28𝑥3𝑑𝑥 − න32𝑥3𝑑𝑥 − න9𝑥2𝑑𝑥 + න7 𝑑𝑥
න28𝑥3 − 32𝑥3 − 9𝑥2 + 7𝑑𝑥
28න𝑥3𝑑𝑥 − 32න𝑥3𝑑𝑥 − 9න𝑥2𝑑𝑥 + 7න 𝑑𝑥
= 
28𝑥3+1
3+1
= 
28𝑥4
4
= 
7𝑥4
7
= 
7𝑥4
1
= 7𝑥4
= 
−32𝑥3+1
3+1
= 
−32𝑥4
4
= 
−32𝑥4
4
= 
−8𝑥4
1
= −8𝑥4
= 
−9𝑥2+1
2+1
= 
−9𝑥3
3
= 
−9𝑥3
3
= 
−3𝑥3
1
= −3𝑥3
= 7. 𝑥 + 𝑐 = 7𝑥 + 𝑐
න8𝑥6 + 7𝑥3 − 7𝑥2 + 4𝑑𝑥
න8𝑥6𝑑𝑥 +න7𝑥3𝑑𝑥 −න7𝑥2𝑑𝑥 + න4 𝑑𝑥
න8𝑥6 + 7𝑥3 − 7𝑥2 + 4𝑑𝑥
8න𝑥6𝑑𝑥 + 7න𝑥3𝑑𝑥 − 7න𝑥2𝑑𝑥 + 4න 𝑑𝑥
= 
8𝑥6+1
6+1
= 
8𝑥7
7
= 
7𝑥3+1
3+1
= 
+7𝑥4
4
= 
−7𝑥2+1
2+1
= 
−7𝑥3
3
= 4. 𝑥 + 𝑐 = 4𝑥 + 𝑐
න5𝑥4 − 4𝑥9 − 5𝑥2 + 4𝑑𝑥
න5𝑥4𝑑𝑥 −න4𝑥9𝑑𝑥 − න5𝑥2𝑑𝑥 + න4 𝑑𝑥
න5𝑥4 − 4𝑥9 − 5𝑥2 + 4𝑑𝑥
5න𝑥4𝑑𝑥 − 4න𝑥9𝑑𝑥 − 5න𝑥2𝑑𝑥 + 4න 𝑑𝑥
= 
5𝑥4+1
4+1
= 
5𝑥5
5
= 
−4𝑥9+1
9+1
= 
−4𝑥10
10
= 
−5𝑥2+1
2+1
= 
−5𝑥3
3
= 4. 𝑥 + 𝑐 = 4𝑥 + 𝑐
=𝑥5
න2𝑥4 − 3𝑥5 − 4𝑥2 + 2𝑑𝑥
න2𝑥4𝑑𝑥 −න3𝑥5𝑑𝑥 −න4𝑥2𝑑𝑥 + න2 𝑑𝑥
න2𝑥4 − 3𝑥5 − 4𝑥2 + 2𝑑𝑥
2න𝑥4𝑑𝑥 − 3න𝑥5𝑑𝑥 − 4න𝑥2𝑑𝑥 + 2න 𝑑𝑥
= 
2𝑥4+1
4+1
= 
2𝑥5
5
= 
−3𝑥5+1
5+1
= 
−3𝑥6
6
= 
−4𝑥2+1
2+1
= 
−4𝑥3
3
= 2. 𝑥 + 𝑐 = 2𝑥 + 𝑐
න29𝑥3 − 30𝑥3 − 10𝑥2 + 3𝑑𝑥
න29𝑥3𝑑𝑥 − න30𝑥3𝑑𝑥 −න10𝑥2𝑑𝑥 +න3 𝑑𝑥
න29𝑥3 − 30𝑥3 − 10𝑥2 + 3𝑑𝑥
29න𝑥3𝑑𝑥 − 30න𝑥3𝑑𝑥 − 10න𝑥2𝑑𝑥 + 3න 𝑑𝑥
= 
29𝑥3+1
3+1
= 
29𝑥4
4
= 
−30𝑥3+1
3+1
= 
−30𝑥4
4
= 
−10𝑥2+1
2+1
= 
−10𝑥3
3
= 3. 𝑥 + 𝑐 = 3𝑥 + 𝑐