If (a,b) be the orthocentre of the triangle whose vertices are (1,2),(2,3) and (3,1), and I1=∫abxsin(4x−x2)dx, I2=∫absin(4x−x2)dx, then 36I2I1 is equal to:
Explanation
Equation of AB is
y−3=1−22−3(x−2)
y−3=x−2
y−x=1
y−1=−1(x−3)⇒y−1=−x+3⇒x+y=4
y−3=2(x−2)⇒y−3=2x−4⇒2x−y=1
x=35,;y=37
I1=∫abxsin(4x−x2),dx⇒2I=4I2
I1=2I2⇒I2I1=2
∴I236I1=72
Explanation
Equation of AB is
y−3=1−22−3(x−2)
y−3=x−2
y−x=1
y−1=−1(x−3)⇒y−1=−x+3⇒x+y=4
y−3=2(x−2)⇒y−3=2x−4⇒2x−y=1
x=35,;y=37
I1=∫abxsin(4x−x2),dx⇒2I=4I2
I1=2I2⇒I2I1=2
∴I236I1=72
