Integral question?

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Answer 1 · 2018-03-01T13:57:42

We have that

#int_-4^5 g(x)dx=int_-4^-2 g(x)dx+int_-2^0 g(x)dx+int_0^5g(x)dx#

Hence

#2=int_-4^-2g(x)dx-2+1#

#int_-4^-2 g(x)dx=3#

So correct answer is B

Answer 2 · 2018-03-01T13:57:59

The answer is #"option B"=3#

Apply Chasles' Relation

#int_a^cf(x)dx=int_a^bf(x)dx+int_b^cf(x)dx#

Therefore,

#int_(-4)^5g(x)dx=int_(-4)^(-2)g(x)dx+int_(-2)^0g(x)dx+int_0^5g(x)dx#

But,

#int_(-4)^5g(x)dx=2#

#int_(-2)^0g(x)dx=-2#

#int_0^5g(x)dx=1#

So,

#2=int_(-4)^(-2)g(x)dx-2+1#

#int_(-4)^(-2)g(x)dx=2+2-1=3#