Question

If H(a, b) is the orthocentre of △ABC where A(1, 2), B(2,3) & C(3, 1), then find \(\frac {36 I_1}{I_2}\) if \(I_1 = \int ^b _ a \,x\,sin (4x - x^2) dx\) and \(I_2 = \int ^b _ a \,sin (4x - x ^2)dx\).

Answer 1

Correct answer is 72

△ABC is isosceles 

⇒ H lies on angle bisector passing through (3, 1) which is x + y = 4 

\(\therefore\) a + b = 4 

Now apply (a + b – x) in I₁