1) Solve the following:
\(\int {\sin x^1/2/xdx}\) (limit from 0 to 1)
2) How many real roots does the following equation have:
x^7 + x^6 + x^5 + x^4 + x^3 + x^3 + x^2 + x^1 + 1=0
I dont have an answer for this question, did it as following .Is it right
Since this is a geometric progression the above expression can be written as
(x^7-1)/(x-1)=0 , now for no value of x this equation is satisfied because at x=1 it will be undefined .therefore no real roots for this equation.
In the second one if I assume that x3 has been typed two times unintentionally, then there are 8 terms in the GP. So, in your approach x8 should come and then you can factorise x8-1 further. Clearly x=-1 will satisfy the equation.
In the first one, it is not clear where exactly is the division sign, also the role of 1/2 is not very clear. You may like to look at the question typing syntax.
Sir, would you please refer to the file attached for the first question.
The integral given \(\int\limits_0^1 {{{\sin \sqrt x } \over x}dx} \) can be brought into the format \(2\int\limits_0^1 {{{\sin t} \over t}dt} \) which is a well known integral and can be solved by numerical method or by series expansion.
PS: The TeX codes for \(\int\limits_0^1 {{{\sin \sqrt x } \over x}dx} \) are \($\int\limits_0^1 {{{\sin \sqrt x } \over x}dx} \)$.