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Evaluate: int(-1)^4f(x)dx=4a n dint2^4(3...

Evaluate: `int_(-1)^4f(x)dx=4a n dint_2^4(3-f(x))dx=7,` then find the value of `int_2^(-1)f(x)dxdot`

Text Solution

Verified by Experts

The correct Answer is:
`-5`
We have `int_(2)^(4)(3-f(x))dx=7`
`:.6-int_(2)^(4)f(x)dx=7` or `int_(2)^(4)f(x)dx=-1`
Now, `int_(2)^(-1)f(x)dx=-int_(-1)^(2)f(x)dx=-[int_(-1)^(4)f(x)dx+int_(4)^(2)f(x)dx]`
`=-[int_(-1)^(4)f(x)dx-int_(2)^(4)f(x)dx]=-[4+1]=-5`
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