20-09-09 Quadratic and Integration....

Solve for real values of x

\left( \int_{0}^{1}\frac{1}{t^{2}+2t\cos a+1}dt\right)x^2+\left(\int_{-3}^{3}\frac{t^{2}\sin 2t}{t^{2}+1}dt \right)x+2=0

Saw this on another forum... not very tough... only looks dirty...

4 Answers

coeff of x is zero sir and the coeff of x² is tan^-1(1+cosa)-tan^-1cosa/sina

one thing that you recognized correctly is coeff of x

can you say something better about the coeff of x^2?

106

Asish Mahapatra ·2009-09-24 20:22:42

coeff of x² is positive and coeff of x=0 as that is odd func.

so no real value of x

coeff of x² is positive
this is because

min value of t²+2tcosa+1 = (4.1.1-4cos²a)/4 = sin²a

which is â‰¥ 0

good work asish :)

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