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show that the sum of the two integrals `int_(-4)^(-5) e^((x+5)^2)dx+3int_(1/3)^(2/3) e^(9(x-2/3)^2)dx` is zero |
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Answer» `I=int_(-4)^(-5)e^((x+5)^(2))dx+3int_(1//3)^(2//3)e^(9(x-2/3)^(2))dx` `=int_(-4)^(-5)e^((x+5)^(2))dx+3int_(1//3)^(2//3)e^((3x-2)^(2))dx` `=I_(1)+I_(2)` Note that in both `I_(1)` and `I_(2)`, function has same form i.e. `e^(t^(2))`. Also `e^(t^(2))` is no integrable. Now in `I_(1)` let `x+t=y` and in `I_(2)`. Let `3x-2=-t`. Then `I=int_(0)^(0)e^(y^(2))dy+int_(1)^(0)(-dt)=0`. |
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