How would I go about proving or disproving this statement?
$$\int_{4+a}^{2a+1} \int_{4a+b}^{2b+1} \frac{6}{ {2a}(b^3+1)^{1/4}} \, {db}\,{da}=-\int_{4+a}^{2a+1} -\int_{2b+1}^{4a+b} \frac{6}{ {2a}(b^3+1)^{1/4}} \, {db}\,{da}$$
How would I go about proving or disproving this statement?
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multivariable-calculus
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1you shoudn't use the same variables for the variable of integration and the limits of the integral. your statement should be wrong: the inner integral is transfered correctly since $\int_a^b f(t) \, dt = F(b)-F(a) = - \int_b^a f(t) \, dt = - (F(a)-F(b))$. By the same rule the outer integral will be wrong (limits weren't interchanged there, but you added a minus anyway.) – 2017-02-22
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0What do you know about how integrals intract with negative signs? – 2017-02-22
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0I think the two are not equal because the negative inverts the limits but the other question I have is whether or not there is a relationship between the two integrals ? – 2017-02-22