Question

if f(x)=|x-1|-2|x+2| , int_-3^3f(x)dx​

Answer 1

Answer:

5

Step-by-step explanation:

∫

−1

4

​

f(x)dx=4 and ∫

2

4

​

[3−f(x)dx=7]

F(4)−F(−1)=4     →(1)

and 3∣x∣

2

4

​

−[F(4)−F(2)]=7

[F(4)−F(2)]=6−7=−1

∴  F(4)−F(2)=−1→(2)  

∫

−1

2

​

f(x)dx=F(2)−F(−1)→(3)

eqn.(1)-eqn.(2),  we  get  F(2)−F(−1)=5

∴  ∫

−1

2

​

f(x)dx=

5

​

  (put  value  in  eqn.(3) )