Integral of Sqrt(x^2+arccos(x)) from 1√3 to 1√3

[Triggy]

Why does
$$\int^{1\sqrt3}_{1\sqrt3} ^5{\sqrt{x^2 + arccos{x}}}dx$$

= 0

 

[itsjustme]

because by this you mean find the area enclosed between the curve and the x-axis between squareroot3 and squareroot3. its the integral of it at squareroot3 minus the integral of it at squareroot3. so if we let the integral function be g(x) your expression says "g(squareroot3)-g(squareroot3)"

 

[Werg22]

And just what is $$\arccos {\sqrt{3}}$$?

 

[HallsofIvy]

triggy, itsjustme's point is that
$$\int_a^a f(x)dx= F(a)- F(a)= 0$$
for any integrable function f (F is, of course, an anti-derivative of f).

Werg22's point is that, since $\sqrt{3}$ is larger than 1, the problem makes no sense as a real valued integral!

 

[George Jones]

Werg22's point is that, since $\sqrt{3}$ is larger than 1, the problem makes no sense as a real valued integral!

My guess is that Triggy made a typo, i.e., Triggy meant

$$\int^{1/\sqrt{3}}_{1/\sqrt{3}}$$

 

[itsjustme]

either that or arctan instead of arccos but i highly doubt it seeing it is 1squareroot3 not just squareroot3