The given equation of line is
\(x–7y+5=0\)
or \(y = \frac{1}{7}x +\frac{ 5}{7}\), which is of the form \(y = mx + c\)
∴Slope of the given line=\(\frac{1}{7}\)
The slope of the line perpendicular to the line having a slope of \(\frac{1}{7}\) is \(m=\frac{-1}{(\frac{1}{7})} = -7\)
The equation of the line with slope -7 and x-intercept 3 is given by
\(y = m (x - d)\)
\(⇒ y = -7 (x - 3) \)
\(⇒ y = -7x + 21 \)
\(⇒ 7x + y = 21\)
If \( (a, b) \) be the orthocenter of the triangle whose vertices are \( (1, 2) \), \( (2, 3) \), and \( (3, 1) \), and \( I_1 = \int_a^b x \sin(4x - x^2) dx \), \( I_2 = \int_a^b \sin(4x - x^2) dx \), then \( 36 \frac{I_1}{I_2} \) is equal to: