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Evaluate by substitution. `int_0^ax(sqrt(x^2+a^2))dx`, a>0Evaluate by substitution....
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Our substitution is `t=x^2+a^2` and our new limits of integration are `t_1` and `t_2`.
`1/2int_(a^2)^(2a^2)sqrt t dt=1/2cdot2/3t^(3/2)|_(a^2)^(2a^2)=1/3(2^(3/2)a^3-a^3)=1/3(2sqrt2-1)a^3`` `
Posted by tiburtius on February 7, 2013 at 10:18 PM (Answer #1)
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